New museum Downtown Miami. I've heard good comments.
It's free every second Saturday of the month!
FIU's art museum used to be a tiny 2-room spot inside the same building as the registrar and several classrooms. These days, they've got one of the nicest museums in town. What's better, it's totally free. The Frost Art Museum boasts two stories and several rooms with rotating exhibits, making it a great place to spend some time between classes (if you happen to go to FIU), or a nice place to take a date on the cheap. Check the calendar in advance and you might even catch a good lecture!
Always has great exhibits and the artist lectures are quite informative. Love the campus too.