Come is a general word used for entering a current place. It can be used for coming
from short distances or long distances.
▶️ My sister lives in London, but next week she’s coming to visit me in Atlanta.
▶️ Our neighbors are coming over for dinner tonight.
▶️ Come here – I want to show you something.
Arrive and reach are usually used for travel. Reach usually implies that the
distance was long, or there was some difficulty in arriving.
▶️ If we catch the 6 AM train, we’ll arrive in the city around 7:30.
▶️ We had been driving for eight hours, and we were exhausted by the time we
reached Miami.
The word get is simply an informal way to talk about arriving or reaching a
destination:
▶️ If we catch the 6 AM train, we’ll get to the city around 7:30.
▶️ We had been driving for eight hours, and we were exhausted by the time we
got to Miami.
▶️ Let’s go to the new shopping center tomorrow. Do you know how to get
there, or do you need directions?
▶️ My brother always takes a nap after he gets home from work.
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.