My choice would be Tony Stark’s place in Malibu.
When we met his arch-nemesis Justin Hammer back in the 80s, Hammer lived on an artificial island that he could move around - the luxury of having your own private island combined with the convenience of a yacht.
“The top of a skyscraper, where Doc Lived, had his secret basement garage…”
How can you have a basement at the top off a skyscraper?
I tend to like “Eats,” the Heckler’s base. Not exactly a calming place, but some great characters, especially Mr. Dude, who the Pope comes to for advice.
Doctor Strange’s sweet brownstone in Greenwich Village always seemed pretty cool. Like, it’s a livable place with a well-stocked library and WHAT THE HELL IS THAT?
Usually the tower’s interior has been depicted as an Escher-like architecture of stairs aligned to different perspectives. It’s also usually implied to be (near) infinite.
Villains always have the coolest lairs. The best may have been Syndrome’s lair on Nomanisan Island in The Incredibles, although I can’t find any good pictures of it.
Another great one is Skullcrusher Mountain.
whups; posted in wrong thread. nevermind me.
The Blackhawks had an Island.
Peter Parker’s apartment back around the time he got married. I like the ordinariness of it. 
Of “special” ones; both Xavier’s original school and Logan’s Jean Grey School were pretty good settings for lots of comics, and Dr. Stephen Strange’s Greenwich Village house with the funky upper window was cool-looking.
For another glimpse of an identical window, look up Will Eisner’s The Spirit.
He has a hidden lair in a cemetery, with the stair leading down to it, going through a grave. His own, of course.
Hourman (in the 1999 series) had his Century of Solitude that he time-traveled to when he wanted to get away from it all.
Apparently, in the *extremely *distant future, people stop numbering centuries and instead give them themes. One entire century is dedicated to Hourman fandom, and he traveled there whenever he needed a bit of ego-boost. (The “…of Solitude” part was not exactly an apt description.)