I'm from Florida but have only briefly visited Miami or driven through it, but...
If the weather is nice definitely check out the beaches! I've never been to a beach in florida that I didn't like. Our beaches are usually a fine white sand.
The Everglades our a very popular nature attraction. I've never been but I've heard great things from my friends who have. Now would be a very good time too since it's winter here. It shouldn't be uncomfortably hot, shouldn't rain, and there will probably be a lot less mosquitos.
I second desertjedi's suggestion of visiting the keys if you have the time and resources. It's a simple lovely drive down that road connecting them and key west is a fun place to visit. It's got a nice historic district too.
If you're into art maybe check out the galleries? I hear Miami has a thriving fine arts culture and the great Miami Art Basel is held there every year in December.