A black hole is simply a quantity of mass that is so dense that it's escape speed is the speed of light. This is bad news for objects that are very close to the black hole (especially if they are inside the "event horizon", the distance at which even light can not move outwards).
However, from a distance, it is for us simply a mass that counts in the total mass of the Galaxy. We would have to count it (as well as the rest of the mass in the Galaxy) when we figure out the speed we need to reach another galaxy.
From our position, the Galactic escape speed is much less than the speed of light (we are well outside the event horizon of our Galaxy's black hole -- tens of light-years outside -- no problemo).
According to Wiki, the Galactic escape speed, at our position, is approximately 1,000 km/s. In comparison, speed of light is close to 300,000 km/s. We only need to go at 0.4% the speed of light to escape to another galaxy.
Of course, we'd want to go faster, if only to get there sooner...
At 0.4% of speed of light, we'd need over 600 million years to get to Andromeda galaxy.