Galaxies are closer together relative to their size than stars; but they're still a few orders of magnitude farther apart than this.
The scale I've seen is: If the sun were the size of a ping pong ball, the next nearest star would be hundreds of miles away. But if the Milky Way were the size of a CD, Andromeda would be on the other side of the room.
Isn't that why/how the Internet was created?