As I believe Haradon mentioned, but which could use further emphasis, you can get anywhere in the universe in an arbitrarily short amount of time, as measured by the traveler. No weird physics is involved here; just get yourself the fastest engine you can, and go. The faster the engine, the sooner you'll get there, from your own perspective.
If you had a fast enough engine, (in the conventional sense of the word
"fast") you could get to alpha centuri (4.6 light years away) in six months
or even less using conventional thrust and acceleration.
The weird physics only comes in when I tell you that this is true from YOUR perspective only; everybody else would see you travelling at sub light speed. But who cares? You'd only have to bring six months worth of food, six months worth of reading material, etc. and as far as you cared, you'd be there in six months.
Of course, as others have pointed out, this isn't particularly efficient; you'd likely be better off going there more slowly and sleeping most of the way.
-GIVE ME IMMORTALITY OR GIVE ME DEATH-