Its true that light takes 2.5 million years to travel to Andromeda, as seen by us who are mostly stationary and not doing the travelling. The thing is though, the faster you go, the more time on board the ship slows down, relative to the outside world. If the ship goes super fast, approaching lightspeed, it would look to observers on the outside that time is almost stopped onboard the ship. Or to look at it another way, from the point of view of astronauts on board the ship, the local shiptime is normal, but the time outside seems to get faster and faster. If the ship travels fast enough, you get to watch 2.5 million years go by outside, at which point you are at Andromeda.

If you are able to reach almost lightspeed, you can reach almost any part of the universe within your lifetime (or even years, or days, if you go extremely close to light speed), but, the universe will have aged by millions or billions of years when you get there. For photons, which actually do travel at lightspeed, the journey is instantaneous, as they don't experience time at all.