Leave it on the counter. Baked goods go stale quickly when refrigerated. Do not freeze it if frosted because when it is thawed the condensation from freezing can make the colored part of the frosting run.

Put it in your freezer.

My mom birthday is Sunday I pick the cake up Saturday evening but don't want my mom to see it want to keep at my neighbors house but do I put it in her refrigerator ? Or just keep it on the counter ?