Don't go to the Miami Seaquarium, it's old and awful.
I grew up in Miami and lived in South Beach for a few years. The Zoo is nice, but the Everglades is a more unique experience. Walking along Ocean Drive on South Beach is lots of fun, and especially pretty with the Art Deco buildings and the lights at night. You can go to David's Cafe and have authentic Cuban food, or News Cafe for a locals experience. Joe's Stonecrab is an (expensive) institution with the best stone crabs in existence. They have their own farm in the Everglades and many restaurants buy from them. Maybe rent rollerblades and skate on the path on the beach side. Lincoln Road Mall is also fun, lots of shops and restaurants.
Boating is also wonderful, the intercostal is cool and the houses on the islands near the port are unbelievable, its right next to downtown, so quite a view. Boat captains would know about the great sandbar areas and it's fun to head south too, very pretty. You can rent waverunners in Biscayne Bay too.
Hope that helps!
Mindy