Believe it or not, you can actually get a half-decent model of the original Enterprise! Flight dynamics are based on the 737, and it's slightly bizarre seeing it take off from a runway, but it looks quite good in the air. I saw it over on Flightsim.com (or nonodes, as we call it), worth checking out some of the additions, improved sound, phaser effects etc.
The other alternative is to check out the Orbiter sim, as they have a few Star Trek addons; I've flown the Delta Flyer up to the ISS on numerous occasions - it's actually the only way you can get up into space anyway. You can find it at
http://www.medphys.ucl.ac.uk/~martins/orbit/orbit.htmlor look over on Avsim.
Live long and prosper.