Regarding the Galaxy: The most well done galaxy in any game I have ever seen is in Frontier: First Encounters, by David Braben. An accurately rendered galaxy, and not terribly difficult to navigate. While travel was different in that game - with discreet warp "hops", it would be not terribly difficult to translate that into trek.
As far as taking too much memory to have "away missions" - this game also rendered the surface of every planet and allowed you to land your ship on any non-gas-giant. The graphics were primitive compared to today, but it is not hard to come up with methods of doing this. The way you do it is with calculated modelling, not pre-rendered. For example, for each planet you have set a level of development, a founding (building) race, size, percentage ocean covereage, etc. Then when the planet is encountered, it is dynamically constructed in memory using these specifications and a random seed. You don't need to pre-fab it all. There are lots of good fractal terrain algorythms, and constructing a city from parts wouldn't be too terribly hard either. Add a capitol city with a government center, plus mission-specific points of interest, and you have the makings of an away mission. This is a very doable scenario. Unfortunately, this method of game writing has fallen into disuse. When games were delivered on floppies and storage sapce was at a premium, this was done in order to save disk space. The possibilities with modern modelling techniques and processing capacities are endless.
The last thing First Encounters added was a realistic planetary model for each solar system. What a joy to play this game - I enjoyed just flying around. Real solar systems with binary and trinary stars, planets that really rotated and orbited around the sun. Moons that really orbited planets.
I can only hope that some day some game company takes up the gauntlet and truly innovates like Mr Braben did. In a Trek game, it would be astounding.