As you approach the speed of light, the rest of the universe contracts to zero size. Even though the andromeda galaxy is 2 million light years away, you could get there arbitrarily quickly by traveling at large, sublight speeds.
For example, if you were traveling at 99.99999999999% the speed of light, the distance from earth to the andromeda galaxy would contract to 1 kilometer, so you'd arrive in a fraction of a second.
At realistic levels of human acceleration (e.g. 1g) the trip to andromeda could still take only less than 30 years.
Edit: The point of all this is that faster than light travel is not necessary. In Star Trek, they say that Warp 10 corresponds to theoretically infinite speed where the entire universe looks like a single point. The funny thing is that's what happens in reality as the speed of light is approached, the entire universe contracts to a single point so every destination becomes near. The whole warp system is superfluous, since the speed of light already corresponds to warp 10.