Several options: New Talax (the asteroid field near the edge of the Delta and Alpha Quadrants), Bajor, The planet in the Delta Quadrant with the 37's descendants (or any other friendly species Voyager encountered - heck, by the 32nd century, the entire DQ could have mellowed to the Federation). Gamma Quadrant (I'm liking the idea the Founders may have joined the Federation at some point, or at least formed an alliance) Qo'nos sounds like a viable candidate too. The Romulans may have joined the Federation at some point too (or at least formed an alliance)... but given how aggressive and powerful the Tal'Shiar was in Star Trek Picard... it doesn't strike me as a particularly viable option (but it IS about 800 years after, so anything could have happened) - though, the Klingons could also be considered 'vicious' compared to the Romulans, and we know they were part of the Federation by the 26th century and participated in combat against the Sphere Builders (but, would that future still occur what with the NX-01 destroying the Delphic Expanse? Possibly... the Sphere builders may have created a new Delphic expanse elsewhere in Milky Way). Albeit, SF headquarters could end up being on a giant starbase/ship which is capable of traversing massive distances and didn't use dilithium or antimatter. Wouldn't it be interesting to see the Yorktown starbase in the Prime Universe in some fashion? Maybe retrofitted into Starfleet Headquarters and capable of jumping through space or having an alternate method of FTL? Its certainly huge enough. Just please, I don't want to see that Terran City ship monstrosity (the Charon). The design is nothing like the Federation might construct... and if it did, it would be FAR prettier.