> In the TV shows and movies, they never seem to spend more than a few days at a time going anywhere at warp speed.
There are a few canon reasons for this:
1) Ignoring special episodes (and all of Star Trek Voyager) where they use a contrivance to hurl the ship tens of thousands of light-years, the working range of a starship on Star Trek is relatively small:
* The distance to the Romulan Neutral Zone, on the outer fringes of Federation Space, is only 28 light years away from Earth.
* Deep Space 9 (so named because it's on the outer frontiers of known space) is 70 light years away from Earth.
* Oo'nos, the Klingon homeworld, is ~100 light years away from Earth.
2) Ship speed exponentially increases as warp factor increases, and by the time the USS Enterprise-D is in service, warp 9 is fast, but not "I need to get there immediately because every plot shown on TV is an emergency" fast. The maximum sustainable speed for the Enteprise-D is warp 9.6, which is 1,909 times the speed of light. This would allow Picard to reach even Qo'nos from Earth in under 3 weeks.
3) With the exception of the JJ Abrams franchise (where they seem to keep going back to Earth after every mission), the ships featured in Star Trek are generally exploratory: between each episode, they'd roam their mission areas performing routine work. The episode plots would generally revolve around them dealing with an issue that happened to be close to wherever they happened to be at the time.
Of course, being a set of TV series and movies, liberties with distances were routinely taken. For example, in the first episode of Enterprise, they say Qo'nos is 4 days away from Earth at warp 4.5, which would place it less than half the distance between Earth and Alpha Centauri, the closest star system.
There are a few canon reasons for this:
1) Ignoring special episodes (and all of Star Trek Voyager) where they use a contrivance to hurl the ship tens of thousands of light-years, the working range of a starship on Star Trek is relatively small:
* The distance to the Romulan Neutral Zone, on the outer fringes of Federation Space, is only 28 light years away from Earth.
* Deep Space 9 (so named because it's on the outer frontiers of known space) is 70 light years away from Earth.
* Oo'nos, the Klingon homeworld, is ~100 light years away from Earth.
2) Ship speed exponentially increases as warp factor increases, and by the time the USS Enterprise-D is in service, warp 9 is fast, but not "I need to get there immediately because every plot shown on TV is an emergency" fast. The maximum sustainable speed for the Enteprise-D is warp 9.6, which is 1,909 times the speed of light. This would allow Picard to reach even Qo'nos from Earth in under 3 weeks.
3) With the exception of the JJ Abrams franchise (where they seem to keep going back to Earth after every mission), the ships featured in Star Trek are generally exploratory: between each episode, they'd roam their mission areas performing routine work. The episode plots would generally revolve around them dealing with an issue that happened to be close to wherever they happened to be at the time.
Of course, being a set of TV series and movies, liberties with distances were routinely taken. For example, in the first episode of Enterprise, they say Qo'nos is 4 days away from Earth at warp 4.5, which would place it less than half the distance between Earth and Alpha Centauri, the closest star system.