I think that the galaxy closest to the Earth, that is, to the Milky Way, is the nebula called Andromeda, which is 2.5 million light years away. Despite this great distance, M31 is visible, and very pretty. Are there any galaxies closer to the Milky Way than the Andromeda galaxy?
At last 80 nearby galaxies are believed to be part of a small cluster called the Local Group.
The three largest members of the Local Group, have their own system of satellite galaxies.
Over 50 galaxies are satellite galaxies of the Milky Way Galaxy and are closer to it than the Andromeda Galaxy is.
The Andromeda Galaxy is actually number 86 in that list of nearest galaxies.
The Small Magellanic Cloud is number 23 and the large Magellanic Cloud is number 19.
The nearest galaxy on the list is the Canis Major Dwarf Galaxy, altough its status as a galaxy is soemewhat disputed.
If the Canis Major Dwarf Galaxy is not actually a galaxy, the next galaxy on the list would become the nearest galaxy. That is Draco II.