Miami, Ft. Lauderdale or Palm Beach. Pick best price. Rent car. Have hotel arrangements/reservations well before you arrive. There are no longer any hotels or motels on the beach in Miami. Everything is condos and not available. The key is to rent a car. This way you can do as you like and go where you want. If you do not know the area, make sure the car has GPS or bring one with you. Stay on major roadways and do not get lost in Miami. Getting lost in Liberty City would not be good.
Note: There are Dolphin game packages available with transportation to the games. This is the best way to go. Hotel and transportation provided. Call the Dolphins ticket office. I think they can help you.