The San Francisco campus - or at least a large portion of it - is actually the USS Athena, a fully-functional starship that can land on Earth, but also go on mission when needed to provide some hands-on training (and, I assume, help a Starfleet that's still spread fairly thin). They talked a little bit more about it here.
As far as I'm aware, Federation HQ remains a giant ship/space station.
Okay yes that would be rad.