I lived in Miami for 20 years, so let me know what you like...pbiflyer is obviously very knowledgeable as well, and has great questions and suggestions.

Viscaya is more than a museum -- it's a renaissance-style mediterranean home built on the bay, complete with maze gardens and Louis XVI furniture. There used to be a renaissance festival there every March, but they killed it (Viscaya itself asked it to move, and that killed it... I was one of the performers).

Bayside is another downtown shopping area that has lots to offer, but we can't really recommend places unless you tell us your likes/dislikes!