I'll name a few, mostly for the lore reasons. Some no longer exist. Got to say that some of the suggestions before me were also great (Niigata Star City comes to mind).
Back in the day, I always liked Kodiak Research Station. A secret LSF HQ in Alaska, way off the beaten path. Built into an asteroid, with extensions and biodomes, surrounded by the green Alaskan nebula and weird ice asteroids. I understand that it somewhat borrowed Willard's aesthetics, but it was still an interesting concept. Back then, there were also Guard Systems belonging to specific NPC factions; and LSF had Ellesmere, that had Grise Fjord Shipyard, with a prototype recon cruiser in the drydock.
During my Gallic Brigand days, I was kind of partial to Boulogne. Back then Gallia had insane population numbers on stations. That, and the description of what's going on the station gave Boulogne some of those sweet Omega vibes from Mass Effect 2. Back then, I don't think that Brigands had (m)any enemies among the Gallic unlawfuls, so it was sort of an unlawful freeport in the farthest reaches of Gallic Core Worlds.
Lausanne Complex used to be a Gallic Royal Intelligence installation in Zurich where they got up to all sorts of nasty research. The funny thing is that Zurich was part of the reason that brought me and a couple of friends into the game back then. "A system between Gallia and RHEINLAND of all places? Got to see it!" We made some Gallic Royal Intelligence characters, but didn't pay much attention to the station at the time. I built up some faction lore that involved mind control, and that's how \*/~ were born. Then the Enclave emerged, and Lausanne with its shady experience also got handed over to the Enclave NPC faction. It was a funny coincidence how player lore coincided withs story developments back then.
P.S. There was also the mysterious Junction Wreck in a once-empty Kansas. For the Order, I'll probably say Battleship Thebes, simply because it was part of version 4.86, which back then was the biggest leap in story and gameplay in years, and tied to the destruction of an iconic planet from single-player, Toledo. A lot of of expectations and inspired RP back then.
