1. My now favourite was mentioned, but I'll mention it again - Monte Carlo Freeport. The whole system is awesome, the connection to a race track nearby fits nicely (Sombs I beg you, add the Provence racing ost already) and overall vibe of Monte Carlo is very compelling to me. And to others it seems.
2.Ames Research Station. If Freeport 11 is the last (neutral) installation on the edge of humanity's reach, Ames is similar. But when Omicrons are scary and dangerous because if harsh conditions and aliens - Kepler bears even scarier nature - one wrong step and you are lost in the darkness that no light can pierce and where Ames is the only safe harbor, constantly fighting for its survival.
3. Shasta Orbital Skyhook. Even though Baffin isn't even near to be popular, its solitude only adds up to the vibe. And I only imagine how cool Shasta would look if it was possible to fully integrate what's written in the infocard.
A couple of my personal favs were already mentioned (Shasta Orbital Skyhook & Niigata Star City, both just really good looking stations) but my overall fav is Ithaca Station. Fortified inside a boulder mound with lots of flavor ships docked waiting to defend and actually fighting intruders as they try to get inside the defenses. I get an thrill just running in there every single time. Feels like running moonshine! Just a really nice stop when coming back from Omegas/Omicrons and you need to drop contraband or repair a radiation damaged hull.
It's not in the game anymore, but my favorite was always Kara Research Station in old Cayman. The spinning gyro on it always fascinated me and I was working towards getting a custom station for a POB of mine at one point with it--though that fell through because of various hurdles. A secondary one is Ames, followed by Barrier Gate Station. Maybe an honorable mention to Ithaca.
I've lost people who meant the world to me...and I'm still doing just fine. I'm coming for everything they said I couldn't have.
Base: Aralsk Complex (Combine of Aralsk Research Station and Aralsk Shipyard)
Why: Have interesting design, for sure. Have some common things like from Freeport 11 or other freeports but in same time have little details that changing perception for this object. Tubes with gas coming out, specific windows on some sides of station and circle which holding most of elements of the station.
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.