Going to Miami Labor Day Weekend w/ Husband - what to do?

We're going to Miami for the first time Labor Day weekend. What are the "must-see", "must-eat", "Miami-esque" places we should go? We're outdoorsy, more relaxed rather than fancy, and wouldn't mind even seeing if there was a game in town?

We're thinking of not renting a car - we don't mind walking, and we're staying on the beach.

Asking from the ones who have been there, done that! :) Any/all req's welcome!