What are the nearest galaxies I can observe? What are the nearest galaxies I can observe using my Telescope? Does it require to be out of the city lights?
The nearest one is the one you are on: Milky Way. It can be seen from any place, as it is all around us.

If you want to actually look at a whole galaxy in a simple view, then the nearest galaxies easy to be observed are the Small and Large Magellan Clouds, and the Galaxy of Andromeda.

There are galaxies nearer that those, but harder to be observed. A quite complete list is at https://en.wikipedia.org/wiki/List_of_nearest_galaxies