We don't see much of the base in "Court Martial" or "The Menagerie", but we do see several things that suggest it is quite large:
- civilian as well as Starfleet presence
- definite architecture in ground facilities; this isn't just a space station or a temporary ground facility or just a simple military barracks
- it has a nice O-club, very nicely appointed office and medical facilities, hi-rise apartment housing, nice concourse, a very grand courtroom, etc.
- Ships stop here for repairs, not just supplies
- The base C.O. is at least a Starfleet commodore in rank