Take an airboat tour or rent bikes to ride in Shark Valley - both will give you opportunities to see gators! You can also do walking tours that are easy for everyone to participate. Be sure to pack sunscreen, water and bug repellent and plan for the drive (approximately an 1HR+ away from Miami Beach)
Wynwood is one of our favorite areas to visit while we're in town. There's a ton of fun breweries and bars with live music and great food. You can also check-out Wynwood Walls. Fun breweries: La Tropical Cerveceria and Veza Sur Good bites: Le Chick Miami, 1-800 Lucky, KUSH and plenty more to choose from It's a quick 15-20 min. drive from Miami Beach so highly recommend the visit if you have the time.
Brickell is the closest thing Miami has to NYC (at a very small scale). It has a ton to offer with great restaurants, bars and shops. it's a 15-20 min drive from Miami Beach depending on traffic.
It wouldn't be a trip to Miami without a trip to South Beach right?