I would agree that the weather in Miami will be a lot better than in CA that time of year.
If you are doing the backpacker thing then there is this place
http://www.theclayhotel.com/ in South Beach. I used to live round the corner from it and had friends stay there. They always said it was good but I never saw more than the lobby.
There are a couple of hostel type establishments for backpackers in South Beach and it is definitely where the action is in Miami at night. There are also some good and inexpensive places to eat but they take some searching out amongst the more glitzy and expensive locations.
Its been a few years since Ive been back so things might have changed but that part of Washington Ave is safe (with the usual disclaimers about keeping your wits about you at all times as you would anywhere else).
I'm getting quite jealous typing this..... have fun.