Come is a general word used for entering a current place. It can be used for coming from short distances or long distances.
Arrive and reach are usually used for travel. Reach usually implies that the distance was long, or there was some difficulty in arriving.
The word get is simply an informal way to talk about arriving or reaching a destination:
Note that we say get to most destinations. But with here, there, and home, we don’t use “to” – we say get here, get there, get home.