The Attic of Justice!

Batman has the Batcave.  Superman has his Fortress of Solitude.  The Justice League has a satellite base.  The Teen Titans have a big T-shaped building on its own island.  The Silver Shield has a fancy estate on top of a fancier underground facility.  The X-Men have something similar but less cool than the Silver Shield's. 

The Sentinels of New Troy currently make their headquarters in a loft attic on the campus of Rathaus University.  The Old Library is more of an archive than a research facility nowadays, and so the mostly unused attic is a perfect place to not draw attention.  Through the tireless efforts of Kepi Aswajan, the Sentinels' trusty secretary, housekeeper, and research assistant, the attic has been fitted with an unlisted phone line, decorated with some surplus furniture, and cleaned up so that it's reasonably comfortable.

The Attic of Justice is accessible through two entrances, a service stairwell that runs from the back entrance of the Old Library to the attic storage area and a door from the Old Library's open bell tower.  The tower and the crenelated roof provide excellent cover for discreet aerial access, and the large gabled windows give the Attic excellent natural light.

To be frank, the Attic of Justice is only two steps above a kids' tree fort clubhouse, but it's a start.