Joey is visiting friends and family on the West Coast this weekend.
The correct preposition is "on" because we use "on" for surfaces. The west coast is a surface. We say "on the coast" just as we say "on the beach" and "on the shore".
As Anupum said, if it were a city that Joey was visiting, then we would use "in". We use "in" for spaces that are restricted, have limitations, or boundaries.
Joey is visiting friends and family in San Francisco.
We use "at" for locations.
He's staying at Tom's place for three days, and then he's staying at his sister's place for four days.
in - places with limitations, restrictions, boundaries
on - surfaces
at - locations