[doublestuff]

Depending on how much time you have, drive to Key West if you can (it's about a 4-hour drive from Miami, can be much longer if you stop a lot). The drive down the Overseas Highway is something everyone should do at least once. If you can spend a night or two in Key West, even better. There are some tremendous dining opportunities in Key West, my favorite being Better Than Sex, a dessert-only restaurant. Reservations usually required at least a day in advance, so plan ahead.
A&B Lobster House and Blue Heaven are excellent.
If you can be there for sunset, every night at sunset there is a sunset festival at Mallory Square.
Key Largo is nice if you want to experience a taste of the keys, perhaps some kayaking, etc. The snorkeling is incredible but would require that you go in a boat. I get seasick in a bathtub, but I just accept that I'm going to be sick and go. The boats are big and if the conditions are right it might be worth checking out. John Pennekamp State park is a great place for snorkeling and kayaking, etc.
If you don't have time for the Keys, and if you like nature, Everglades National park is worth driving through. Stop at a Publix or somewhere before you go and get some sandwiches, etc. It's 40 miles IIRC from the park entrance to Flamingo at the end of the road, and lots of places to stop and observe, walk boardwalks, etc. Plan for a full day, if you try to zip in and out in an hour it's probably not worth it. Mosquitos should be minimal this time of year but will possibly still be active around dusk. The sun will be brutal even if it's cool so bring sun protection.
And +1 on Oleta River State Park. One of my favorite mountain bike trails, and kayak and stand-up paddleboard rentals available there. Nice place.