(covers information from several alternate timelines)
This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
The Fleet Museum (or the Starfleet Museum), was a museum on Earth, originally run by the United Earth Starfleet, and later the Federation, in which historic vessels or notable objects were placed on display following their decommissioning.
In the first draft script of "Relics", the Fleet Museum was said to be "at Memory Alpha." This placing of the museum was omitted from the installment by the time the final draft of the script was issued. 
Originally, the Starfleet Museum was to have been depicted in the anti-time future portrayed in Star Trek: The Next Generation series finale "All Good Things...". It was visited by Jean-Luc Picard, Data, and Geordi La Forge. Among its collection of ships, the museum contained the USS Enterprise-D, which the visiting threesome intended to commandeer in order to go on a mission Picard felt they needed to undertake. The group was given a guided tour of the facility by a tour guide who didn't know who they were. Just as the three visitors were about to leave, Admiral Riker and a team of security officers entered the museum, though the group ultimately departed on their mission anyway. (The Fifty-Year Mission: The Next 25 Years, p. 285)