The safest way to avoid detection in stories is always, well, right under the enemy's nose — the last place they'll ever think to look.
This is true even if the antagonist or whoever the hero is avoiding has all his forces concentrated in an easily avoidable heavily armed complex. Despite the fact that the Sword of Plot Advancement is not to be found there, the hero must encounter the Damsel in Distress somehow.
Even when it would make more sense to avoid the enemy stronghold altogether, the seasoned marksmen who swarm the wilderness are always much more likely to capture our heroes if they attempt to sensibly bushwhack away from the enemy camp, whereas the soft green recruits at the main gate would never imagine someone walking up to the Front Door.
This may extend to...:
Literally walking up to the Front Door, usually disguised as filthy peasants. ("these aren't the droids you are looking for.")
Harry Ashworth in Delenda Est figures out a way to steal someone's wand, while they're holding it, without them even noticing it's gone. This skill comes in handy when Harry steals Voldemort's wand in the middle of their duel.
Star Wars does this on several occasions, most notably when Han hides by sticking the Falcon on the back of a Star Destroyer.
Well that bit was justified because the Falcon got lost among the many greebles covering the star destroyer, even for some viewers it was hard to spot.
Although the biggest one, in light of the prequel trilogy, still has to be the decision to hide Luke on his father's home planet under his own name with his only known relatives. Obi-Wan was banking a lot on the idea that Vader would never want to go to Tatooine ever again.
There's also a theory mentioned in one of the books that Obi-Wan had actually put him there as bait to lure Vader in for a final confrontation.
In the movie version of The Two Towers, Pippin suggests this as reason for Treebeard to take him and Merry back towards Isengard; of course, he had other reasons for wanting Treebeard to see Isengard close-up.
Pippin: "If we go south, we can slip past Saruman unnoticed. The closer we are to danger, the farther we are from harm!"
Treebeard: "That... doesn't make any sense to me! Then again... you are very small. South it is, then!"
Even funnier, in The Cannonball Run, they sneak a known race participant (Burt and Dom's ambulance van) through a road block on the back of a "low-boy" carrier, covered only with a tarp and looking exactly like a van covered with a tarp.
Carry On Spying. The headquarters of the evil S.T.E.N.C.H organisation is right under the headquarters of the British Secret Service where the spies started their mission. After the Elaborate Underground Base blows up, the heroes take the elevator to the surface and emerge from a closet in Da Chief's office.
This is explicitly how Sam and Frodo succeed. After all, who in their right mind would take the one artifact Sauron needs to rule the world right to his doorstep? Tolkien at one point tried to make up an excuse for them to sneak into Minas Morgul, but thought better of it.
In The Sherwood Ring, British soldier Peaceable Sherwood takes his hidden militia to crash for the winter at...the shut-up-for-the-war house of the soldier assigned to capturing him, Richard Grahame. Richard is unpleasantly surprised when he makes the mistake of coming over to the house to rummage around for a Christmas gift for his girlfriend.
The title character of Captain Caution, an American privateer, insists he doesn't believe in taking chances. His French friend is incredulous: sailing right into a British-held port and anchoring where the fort's guns will have a perfect shot at him isn't taking chances? Of course not; since he made himself so totally vulnerable to them, the British knew he couldn't be an American coming in to capture one of the ships already in port. And that night, he snuck a crew aboard....
In Harry Turtledove's Great War trilogy, a Confederate submarine commander is able to sail, unsubmerged, within sight of a Union fleet at New York City, protected only by audacity and the fact that the Confederate national flag (as opposed to the well-known battle flag) looks a lot like the Stars and Stripes from a distance.
Turtledove has also featured Jewish characters in other series escaping persecution in Nazi Germany by joining the Wehrmacht or even the SS under a false identity.
In the first Enola Holmes book, Enola, a runaway, is discovered by her brother. When she shakes him again, he spends all night out scouring the city for her, but she successfully escapes by hiding in his house. (And, when she departs, she's able to use some of his disguise supplies to ensure she won't be spotted.)
In Something Wicked This Way Comes, Jim and Will hide in a sewer grate not more than ten feet away from where the Circus of Fear is parading with the reasoning that the carnival folks won't think to look in so obvious a place. They still have a couple of very close calls, though, and would in fact have been discovered by the Dust Witch's Super Senses if Will's father Charles hadn't intervened.
Ruanek: “Audacious, hells, yes! But how in the name of all those hells are you going to get in? Just walk right up and order the gates to open?”
Sultan Mehmed, Vlad Tepes' Islamic enemy in Count and Countess, easily evades all of Vlad's military plans just by hiding out in a church town in the middle of Romania. Vlad does catch up with him in the end.
In the Mistborn trilogy, the protagonists choose to stage their revolution right in The Empire's capital city. The argument is that it's the last place anyone would expect them to do it, and also that it has the most resources for their use.
Snakehead (the seventh Alex Rider book), Alex is trapped on a boat filled with guards searching for him, and it'll be hours before they reach shore and he has a chance to escape. He goes for Refuge in Audacity and spends hours hiding under the villain's bed.
In A Song of Ice and Fire Bran and his company hide from Theon Greyjoy by doubling back and hiding in the crypts under Winterfell.
In one of the Borribles novels, one of the recruits for a new adventure is noted for the clever place he's made his hideout, to avoid the Borrible-hunting police: he lives in a disused basement underneath the police station.
Inverted in Buffy the Vampire Slayer: It is revealed that the Hellmouth is in fact located directly underneath the library where Buffy and the Scoobie Gang hang out and make their plans to stop the bad guys' plans. Given that The Master was trapped in the Hellmouth for all of the first season, it is thus inferred that the Big Bad had been hiding under the heroes' noses the whole time, though it never seems like he's aware of the fact.
Comes up again in the last season in the final episodes. Buffy has a verbal sparring match with Caleb at the rebuilt high-school (the site of the Hellmouth once again) and realizes that the villains SHOULD be fortifying the position in preparation for opening it up and letting out the army of super-vamps. But they aren't. Why? Because they have fortified an old winery where they had already sprung a trap on Buffy and the potentials. Again, why? Because there really is something even more important to the coming battle buried right under the winery.
In the Supernatural episode "What Is And What Should Never Be", Dean takes Wishverse!Sam to the djinn's lair to confront the djinn, and at one point they are literally hiding under the djinn's nose as they hide under an open metal frame staircase as the djinn walks up the steps.
In Hogan's Heroes, this trope is the only half-way plausible explanation of how Hogan's headquarters could stay hidden beyond manipulating Col. Klink and Sgt. Schultz.
Assassin's Creed IV: Black Flag: In the modern day portions of the game, you (as the point of view character) interact with a cell of Assassins that's hiding from the international Templar manhunt targeting them by working openly in the lobby of Abstergo Entertainment, a subsidiary of the very company that is the front for the Templars.
A Corollary Two example in Bob Defendi's podcast audiobook ''Death By Cliche''. It's even Lampshaded somewhat by the main character. Given that the entire thing is a deconstruction of bad GM-ing and poor storytelling, this isn't particularly suprising.
Inverted in Vaguely Recalling JoJo, the villain DIO is constantly following Jotaro's group but they don't seem to spot him until the plot calls for it.