At the end of the first Avengers movie, we saw Stark Tower showing battle damage and all of the letters from the STARK name all falling to the wayside but the big A. Of course, this was a precursor to the coming of AVENGERS TOWER that was built by Tony Stark to house the newest incarnations of the comic book Avengers.
But the Tower is just the latest place that the Worlds Greatest Heroes have called home.
In the beginning, the Avengers stayed where most Avengers stayed: at the Avengers Mansion. This mansion was, of course, the brain child of Avengers co-creator, Stan Lee.
'There was a mansion called the Frick Museum that I used to walk past. I sort of modeled it after that. Beautiful, big, so impressive building, right on Fifth Avenue.'
890 Fifth Avenue is 1 East 70th Street (the address given in the comics as the Avengers Mansion location) is actually the address of the Henry Clay Frick House that holds the collection. This is an impressive block sized mansion.
In the comics, the Mansion was originally Stark Manor; the home of Tony's parents. His parents long dead, he donated it to the Avengers for their use. Also donated to the cause was a household fixture: the butler Jarvis.
Yep, in the old school comics, Jarvis was a person; Edwin Jarvis. He had been with the family and was, then, with the Avengers in some form till the present day.
The mansion has been destroyed twice. The first time was in Avengers: Under Siege (Avengers, Vol. 1; 270-276) when a huge grouping of Masters of Evil, led by Baron Helmut Zemo, attacked the Avengers and destroyed the Mansion and beat Hercules into a coma among other things before being repulsed.
With Zemo getting a role in Avengers: Age of Ultron, you might do good to remember this period of Avengers history. (It tends to repeat itself on the big screen: hint...hint)
While the Mansion sat in ruins, the Avengers moved to HYDRO-BASE:
'Hydro-Base is a floating seacraft disguised as a natural island floating off the coast of North America outside US territorial waters. Its first known user was the mad ecologist Dr. Herman Frayne (aka Doctor Hydro) who used it both as a laboratory and an airbase on which to land hijacked planes. Doctor Hydro planned to turn the planes’ passengers into amphibious people, using Terrigen Mist he acquired from the renegade Inhuman Maelstrom'
The former mansion site became known as AVENGERS PARK and was not used as a base. Hydrobase was also destroyed in Avengers #311
Later, the Avengers built a new headquarters on the site of the Mansion and resided there until it was destroyed by the Gatherers, a team of alternate universe Avengers.
This replacement Mansion would survive various assaults until, in the "Avengers Disassembled" storyline where there was an explosion that killed some current Avengers members. It was at this time that Avengers moved on to Stark Tower. While initially intending to use the top three floors of the Main Tower as his bachelor pad, Stark gave the floors over to the Avengers as their base of operations. Longtime caretaker of the Avengers Mansion Edwin Jarvis was asked to resume his duties in the new location.
During the events of the Fear Itself storyline, Thing (possessed by Asgardian magic and a hammer) tossed his hammer through Avengers Tower, bringing it down onto Red Hulk. A new Stark Tower was later built on the site of the original. The structure currently acts as the headquarters of the Avengers.
Of course, in the movies, Stark tower became the focal point of the fighting between Loki and the alien invasion and the Avengers.
In Iron Man 3, we see plans being made for a new tower. And, just recently we have new pics of the future Avengers Tower for AGE OF ULTRON.