Do any Trek ships have the capability to maintain a fixed position the same way a space station does? Not just standing still, but fixed with stakes in the space ground, so to speak? So like a space RV with starship capacity. It would be an interesting idea for a show - a moving station you could change the location of each season, and deal with different local issues to whatever region you happen to be parked in.
They somehow moved the late 23rd century Earth Spacedock before the end of the 24th century to another Star system to become the Fleet Museum.
The Odyssey/Yorktown ships from Star Trek Online would probably fit the bill. Though one would be taking them away from whatever their usual duties are.
While not a Trek-specific example, the non-military jumpships in Battletech do essentially operate this way, because their drive cores make up about 85% of their total mass and they're solely intended to transport smaller craft to other places. A civilian jumpship that's not actively in transport will typically be stationary, and usually recharging the core via a solar sail, and it only has station keeping drives. No means of sublight maneuvering. Warships and military vessels, by contrast, are equipped to maneuver like a typical ship does.
The Galaxy-class could probably do that if they were used as deep space explorers as designed. Act as a temporary starbase far beyond Federation space for smaller Federation science vessels.
"Thrusters at station-keeping". In other words, "hold us in place". Like a space station. Done properly, the Galaxy-class can essentially be a mobile support facility for other ships.
A pint sized version, yeah. And since a Galaxy Class is basically a small town in space, it would be perfect for repurposing.
Apparently that was just a standard space station design, because we saw one as Starbase 74 (albeit much larger so the 1701-D could fit through the doors) around Tarsas III in "11001001".
Yeah... remember, though, that a Galaxy Class starship is 42 decks high and 700 meters long. Something that big could easily do the work of a space station!
Or use a "Ross Class" Saucer section. Spoiler: Ross Class Saucer vs Galaxy Class. Circular Saucer's are easier to work with than Elliptical Saucer's.
The Galaxy-class has "mobile space station" as part of the purpose of the ship in the TNG Tech Manual. Through TNG, we often see the Enterprise on a mapping mission, studying a nebula, assisting in terraforming or colonization, etc. When this happens, the ship is parked in orbit or relatively stationary for more than the space of an episode, and other ships and shuttles will come to THEM instead of the ship moving around. In this sense, most Federation starships will operate as a stationary element from time to time, and will be equipped to do so. Even when the ship is moving, it remains a mobile installation and allows for policy and force projection in a region of space, just like an aircraft carrier for the USN. Mark
Project a low level warp field around the target (aka, the station itself would be able to do that) to lower its inertial mass, then have several ships establish tractor beams on it and Warp it to the intended destination in another star system. Alternatively, since most SF technology is modular, its possible the top end of the spacedock can be detached from the lower bit, and then both can be moved independently with other ships. Ds9 was able to lower its inertial mass to nothing using a low level subspace field and use thrusters to move itself to the mouth of the Wormhole in under a day. The spacedocks also have thrusters for maintaining their orbital position, and because a spacedock was fully operational (unlike the patched Ds9 from the opening of the series), it would likely be able to change its location in a given star system by itself much like Ds9 did. Apart from that, its possible that later starbases were equipped with Warp capabilities so they can move themselves. I don't know if the new spacedock in the 25th century in Earth's orbit (the one from Picard) has Warp capabilities... possibly not... but anything from late 25th century or early 26th century might. Yes, but one of the reasons the Galaxy class was so big was presumably so it can be in deep space for long stretches of time and conduct exploration. In fairness, a Galaxy class would likely be on the level of a mobile Outpost... but not a starbase (which is technically much larger). It would definitely still be useful to act as a 'staging area' for smaller ships... but Starfleet should really give it an industrial replicator or several to be able to service other ships and create a self-sustaining environment.
O'Brien got DS9 to break orbit under its own power in order to move it into a defensive position near the wormhole, although not under warp. I know this is a bit in reverse from the OP's original question, but the precedent has been set there.
Well, they have a circular planform, so it couldn't be based on the Galaxy. From Memory Alpha, "Sternbach has suggested the saucers may be recycled from decomissioned vessels, perhaps Ambassador-class or similar."