Wich Avengers headquarter did you like most? The classic one? Stark Tower? the micro space station (Secret Avengers)? The infinity one (Mighty Avengers)? Others?
I'm still a fan of Avengers Mansion, even if it isn't practical to have a headquarters in the middle of densely-populated Manhattan (although Stark Tower is even less practical because the whole tower could fall over or collapse if attacked).
For a good mix of practicality and accessibility, I do like the Triskelion idea. What I don't like about the Triskelion is the allegiance to SHIELD. The Avengers should be their own organization. You could also say the same thing about the Triskelion as I used to say about the X-Men's island base - that if attacked you have no place to fall-back to, because you're surrounded by water.