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
The obvious answer is our own, the Mikyway. The only problem is, Where you are in the world? We all will see it differently, many factors play into this, your elevation,city lights,e.t.c One of the biggest problems is light, it has plagued astronomers for years. Depending on how good your telescope is, the next closest galaxy to us is the Andromada galaxy with a good telescope you will be able to see it. You may also be able to view the sm. And lg. Magellan clouds with a larger telescope, remember the better equipment you have,the more you will be able to see. More farther,clearer and be able enjoy more than just galaxies.