"This is Petalburg. The warm weather makes the locals laid-back and happy. Wow, and talk about unique personalities... Very... individualistic, to put it nicely. Or, not so nicely... Downright kooky..."
Marie & Gali has Hubble Gali, populated by deceased scientists.
The Stellar Six has a town made of a series of bazaars and shops, and everyone seems to not only get along extremely well, but most of the main cast have known everyone there since childhood, and everyone (for the most part) gets along.
In one of the Fullmetal Alchemist novels, Ed and Al arrived in a desert town named Wisteria where everything seems extremely happy and kind, and the main female character of the novel, Ruby, insists it's the greatest place ever. Unbeknownst to the brothers at first however, is that the poor of the village, at the behest of the mayor, are sold into slavery.
Just try to name a town in Earthbound that's not this. Go on, we'll be waiting.
Well, except the overpriced tourist town of Summers.
And Fourside, the big city.
And Moonside, the other big city.
Saturn Valley totally counts, though.
Mother 3 has Tazmily Village, which is arguably a Deconstruction. It's a Quirky Town because it's cut off from all other civilization. When outsiders start showing up, it quickly becomes less quirky and a lot less idyllic.
Greenvale in Deadly Premonition. Some of the townsfolk are downright goofy, which just adds to the Mood Whiplash regarding the horrific murders you investigate.
City of Reality, full stop. For starters, their mayor is a bunny rabbit (actually, what looks like a living sock puppet of a bunny rabbit, and that's not just an art style!). Hawk even goes to great lengths in order to test how close it is to being a Town with a Dark Secret, thinking that secret is pent-up rage.
Life Sketch takes place in Hannah, Montana, where vampires, zombies and dragons are commonplace and nobody seems to bat an eye when people go out in public in full cosplay regalia.
Ditto for Vermont, often seen by those on the East Coast as Portlandia stretched over a whole state.
College towns in the United States. Other countries tend not to have these, as their universities were built in major cities.
Salem, Massachusetts: Where there are more occult shops and people walking around in robes than Diagon Alley.
Southport, Merseyside, United Kingdom: Pretty much this Up to Eleven - and this was lampshaded by a local newspaper, and the subject of a Take That by a Mancunian newspaper.
Residents of Austin, Texas, have made "Keep Austin Weird" their motto. While as a state capital it hardly qualifies as a "town", it should be noted that Austin is home to the University of Texas's main campus.
Eureka Springs, Arkansas, is definitely a quirky place. Victorian aesthetics, highly popular with artists, Pagans, and LGBT individuals. Its aerial map is a spider trail that loops wildly, but in spite of this, has almost no traffic lights. It also boasts the World's Largest Tuned Musical Windchime.