If you want a star trek based answer in warp speed, this site is for you
http://www.ditl.org
It says getting to the Andromeda galaxy ( 2 million light years away ) at warp 5 (9,356.9 Years), warp 9 (1318.9 Years).
Here another thing to think about, if you used borg tranwarp technology, then the same trip would take from 1.5 hours at the fastest speeds to 136.6 years at it's slowest. Really interesting when considering if we would develop technology to make humans travel in other realms (Hyperspace), maybe one day but not today.