The US has many nicknames, since each state has an official nickname and a few fan nicknames.
Murika/Murica/Mrkh/Freedomistan
Technically, the usual parlance of calling the USofA 'America' is a nickname.
A popular, derisive nickname for the country is 'murrica (as if one is trying to emulate a deep, coarse Southern dialect. Mostly stems from the notion that the most outspoken patriots are angry rednecks.
Englishmen will sometimes call the residents of the above country "Merkins". This sounds very much like "Americans," but on the other hand...
The proper Canadian response to being called "America's hat" is to call the USA "Canada's underwear." As for calling Canada "the Great White North", well... they call the USA "the Dark Empire of the South".
Hampton Roads metropolitan area: The 757; The 7 Citiesnote Referring to the seven cities that make up the core of the metropolitan area: Norfolk, Virginia Beach, Hampton, Portsmouth, Chesapeake, Newport News, and Suffolk.
Norfolk: The Mermaid Citynote As the city is filled with mermaid statues.
Northern metro (Newport News, Hampton, Poquoson, Williamsburg, plus James City & York Counties): The Peninsulanote This part of the area sits on the Virginia Peninsula.
Southern metro (Virginia Beach, Norfolk, Chesapeake, Portsmouth, Suffolk): The Southside
Portsmouth: P-town
Green Bay: Titletown note After The Packershumiliated the New York Giants in the NFL Championship of 1961, and even more so after their three straight NFL titles from 1965–67
Houston: Space City, H-Town, Clutch Citynote originally applied to the Houston Rockets after their two NBA titles in the '90s, but now also applied to the city as a whole
Indianapolis: Naptown, Circle City, the Crossroads of America, Indy
Milwaukee: Brew City, Mil Town, and occasionally, The Brew or The Mil
Minneapolis/Saint Paul: The Twin Cities. Minneapolis itself is "the Mill City" (it was an early center of the milling industry) or "the City of Lakes" (guess why).
Nashville: The Athens of the South note for its many universities, Music City, Nashvegas note mostly used sarcastically by residents, in reference to the many ill-mannered tourists who visit for bachelorette parties and the like, and Smashville note coined after the Nashville Predators' Stanley Cup run in 2017
Philadelphia: The City of Brotherly Love, Philly, Illtown (negatively, Killadelphia, although that's dropped off since about 2000).
Pittsburgh: The Burgh, Pikksburgh (pronunciation with the regional accent)
Portland: The City of Roses or Rose City (official), Stumptown, Bridgetown or Bridge City, Beervana, Rip Citynote usually used in the context of the city's NBA team, the Trail Blazers
Starkville, Mississippi:note home to Mississippi State University Starkvegas
California is often given Russian-style nicknames by conservatives reflecting its perceived "commie" leanings, such as Kalistan, the Socialist Republic of Kalifornia, etc.
In Chicago, the sculpture named "Cloud Gate" is universally known as The Bean... Much to the artist's annoyance.
Also in Chicago, the newly-renamed "Willis Tower" is still the Sears Tower. We don't care who owns it now or whether Sears Roebuck is on the brink of bankruptcy, it's still the Sears.
Chicago again, the Marina Towers highrise is sometimes called "Wilco Towers", having appeared on the cover of Yankee Hotel Foxtrot.
Canada: The Great White North, America's Hat, Soviet Canuckistan.
Toronto - T.O., Hog Town, The Big Smoke, The Center of the Universe, T-dot
The city proper and its suburbs have separate nicknames based on their telephone area codes. The city proper is The 416, and the suburbs are The 905. Although each of the codes is now overlain with two distinct area codes, the nicknames are still used, since most phones in each area still have the original codes.
More recently, the city proper has picked up the added nickname of The 6, popularized (though not coined) by Drake. It comes both from the last digit of "416" and the six municipalitiesnote the former City of Toronto, Etobicoke, Scarborough, York, North York, East York that were merged by the Ontario provincial government in 1998 to establish Toronto's current borders.
Ottawa - Bytown, The Hill, Beavertown.
Hamilton - Steeltown, The Hammer.
Sudbury - Nickel City, Laketown, The Sudz.
Thunder Bay - Lakehead, TBay, The Bay, West Finland.
Winnipeg - Winterpeg, The Peg, Chicago North.
Moose Jaw - The Jaw, Jawtown, Little Chicago.
Calgary - C-Town, Cowtown, Stampede City.
Edmonton - E-Town, The Big E, The Chuck, Deadmonton, Redmonton, Edmonchuck,note also spelled "Edmonchuk"; a reference to the city's large Ukrainian–Canadian community, with "chuk" being a common element of Ukrainian surnames River City, The City of Champions.
Nova Scotia: The Holy Land, by Scottish-Americans, especially those in the Northeast.
Vancouver - Vancity, Rain City, Raincouver, Terminal City, Hollywood North, Vansterdam, Lotus Land, City of Glass, No Fun City.
In downtown Vancouver, just outside one of the skytrain stops, is a sculpture universally referred to as the big ball of tin foil.
Saint John, New Brunswick - The Port City, Canada's First City
Monterrey: La Sultana del Norte (The Sultaness of the North)
Also known as La ciudad de la carnita asada' (City of Barbecue), because people in northern Mexico in general are fond of hosting barbecues.
Aguascalientes (both the city and the state): La Tierra de la Gente Buena (The Land of the Good People)
And, in a very derogative way, it's sometimes nicknamed La Tierra de la Gente Buena... Para Nada (The Land of the Good... For-Nothing People) because of the perceived lazyness of their people there.
Jalisco: La Tierra del Mariachi (The Land of the Mariachi) since Mexican Mariachi is said to have begun there.
Its capital city. Guadalajara, is nicknamed La Perla de Occidente (The Pearl of the West); the municipality of Zapopan, which is the west side of the Greater Guadalajara area, is known as La Tierra del Maiz (Land of the Corn).
One of the (in)famous neighborhoods, San Juan de Dios, is nicknamed in Guadalajara as Taiwan de Dios since there's a sizable Chinese community there, and lots of stores that sells Chinese products.
The city's strong LGBT community has also created the nickname Donde se dan los hombres (literally "Where men are plentiful", but figuratively "Where men hump each other").
Mexico City: La Ciudad de la Esperanza (The City of Hope) and outside the city (and inside too) it's nicknamed Chilangolandia (Chilangoland, since the people from Mexico City are nicknamed Chilangos in a pejorative way).
The nickname "The City of Hope" was added by current president Andrés Manuel López Obrador, so it's a more recent nickname. The more popular one is "The City of Palaces", and how!
The Mexico City neighborhood of Tepito (which is considered the Mexican version of the New York's Bronx) is nicknamed El Barrio Bravo (The Tough Neighborhood).
The northernmost town in Mexico, officially Vicente Guerrero but more commonly called Los Algodones, has come to be known by Americans (and to a lesser extent Canadians) as "Molar City". Reason? The town of under 7,000 near Yuma, Arizona has about 600 dentists working in about 300 different practices, with about 80% of the patients Americans and virtually all the rest Canadians. Essentially all of the dentists are bilingual, and most if not all of the clinics have US telephone numbers. The main draw is that major dental procedures are a fraction of the cost in either the US or Canada. For a fuller explanation, see this 2019 story.
South America
Guatemala: Land of the Eternal Spring
Peru: Land of the Incas
Colombia: Land of Christopher Columbus (the name Colombia derives from the Spanish reading of Columbus, Colombo). Cocainistan thanks to its infamous role in the drug trade.
Also, but in a pejorative way, is nicknamed in Latin America as "The Israel of South America", being one of the few Latin American countries that is a staunch American ally, compared with almost everyone else in the region, and also having one of the biggest armies of the region, due to the guerrillas and drug trafficking.
Ukraine: The Bread Basket of Europe, Stalkeristan/Vodkastan/Chernobylistan/Cheekibreekiistan
Russians have their own set of nicknames (almost all of which are derogatory, see this Wiktionary entry for examples) for Ukraine. One of them is "Country 404", which is used to mock Ukrainenote 404 is HTTP status code for "Page does not exist" — therefore implying that Ukraine "does not exist"; in other words, in the eye of Russia, Ukraine does not count as a sovereign nation. The nickname is a response to the political upheaval that led to President Yanukovych's ousting and the installation of President Poroshenko, undermining Ukrainian sovereignty in Russian perceptions..
Italy is sometimes referred to as "The Peninsula", despite not being the only peninsula evenin the Mediterranean. Italians themselves call Italy Il Bel Paese ("The Beautiful Country") when they're feeling patriotic, or Lo Stivale ("The Boot") referring to its shape.
Following the "boot" imagery, Apulia is sometimes called "The Heel".
Rome: The Eternal City, Caput Mundi (Latin: Capital of the World)
Venice: The Queen of the Adriatic, The City of Masks
Ireland itself (the island, that is) is regularly called "The Emerald Isle".
County Kerry: The Kingdom (especially with respect to Gaelic games, the island's traditional spectator sports)
The Spire of Dublin, a huge monumental spike practically in the centre of the city, has picked up numerous nicknames (common for public art in the city): "The Spike", "The Spire in the Mire", "The Pin in the Bin", "The Nail in the Pale"*(the part of Ireland that was directly controlled by the English government in the Late Middle Ages, with Dublin at its centre, was known as The Pale, a term still used today to refer to County Dublin, often in a pejorative context), "The Stiletto in the Ghetto", "The Stiffy by the (River) Liffey", "Bertie's Erection"*(referring to Bertie Ahern, who was Taoiseach when the monument was completed), and likely more.
France is often nicknamed "l'Hexagone" by multiple French news channels, because of, well, its hexagonal shape. By extension, the adjective "hexagonal" is often applied to anything made in France.
People poking fun at its modern military record and history of failing to meaningfully apply effective force call it Surrenderistan.
Paris: The City of Love or The City of Light
United Kingdom
The South London district of Newington is far more commonly known as "Elephant & Castle", to the extent that even Transport for London call it that. The name comes from the fact that one of London's several "Elephant & Castle" pubs stood there (there's still a pub of that name there, but whether it's the original or a successor thereto is unknown). Several explanations for where the pub name comes from have been proposed, but the popular one that it is derived from "The Infanta de Castile" has little going for it.
30 St Mary Axe, London is rarely referred to by its address or its official name, the Swiss Re Building as, due to its distinctive shape, most people call it The Gherkin. It's unlikely that this will ever change. Though given how ridiculously phallic the thing looks the owners should count themselves lucky it isn't nicknamed something much worse.
Other buildings in the area have received similar nicknames such as "The Shard", "The Walkie-Talkie" or "The Inside-Out Building".
Africa
Post-Apartheid South Africa: The Rainbow Nation.
Asia
Afghanistan: The Graveyard of Empires (due to the Afghans' record for defeating every foreign power which tries to occupy them, unless you are the Mongols) Trashcanistan, according to one source, on account of how destruction is more common than function.
The desert areas are known as "The Red Centre".
Also called Nopeistan for its infamously terrifying wildlife and weather.
China is nicknamed by their own citizens as The Heavenly Kingdom. (天朝/tiāncháo)
In the early days of the Cold War, U.S. media liked to refer to the People's Republic of China as "Red China", presumably in an effort to suggest that it was illegitimate and "not real China". During the same time period, Taiwan was referred to as "Free China", which was quite funny since it was a military dictatorship at the time.
Kuwait is nicknamed by their own citizens as "Q8", which is pronounced in the same way as the name of the country. Invadedistan.
Japan: Land of the Rising Sun. Sometimes called Hentaiistan playfully.
Korea: Land of the Morning Calm
Under the isolationist Joseon Dynasty, Korea become known as "the hermit kingdom". In more recent times, that term has been applied to North Korea.
Pyongyang: Jerusalem of the East (pre-communist nickname, referring to the successes of Christian missionaries in the city)
Oceania
New Zealand: Land of the Long White Cloud, The Shaky Isles, Australia's Canada. Sometimes called Sheepistan for its great ovine herds, or Tolkienistan for being where the LOTR and Hobbit films were shot.
Auckland - People from Auckland are officially titled 'JAF As' (Just Another F*cking Aucklander).
Wellington - New Zealand's version of 'The Windy City'
The North Island - The official title of the North Island in Te Reo Māori is 'Te Ika a Māui' (The Fish of Māui).
The South Island official title of the North Island in Te Reo Māori is 'Te Waipounamu' (The Waters of Greenstone). It is also sometimes called 'Te Waka o Aoraki' (The canoe of Aoraki).
