Hotel Lobbies
Hotel lobbies are good places to take photos as well. We're not going to list any specific hotels, but if you decide to take this route make sure to call in advance to make sure you're allowed to take photos there.
Umbrella Photos
If all else fails, just pick up some umbrellas and take photos outside where you originally planned. There are lots of ways to get creative in the rain to make sure prom is still fun despite the bad weather.