Try Expedia or Hotels.com for a search. There have been a lot of good reviews on the Holiday Inn near the port of Miami. I would probably opt for something near south beach. There is lots to do in Miami, the Crandon Park Zoo, the Miami Seaquarium, Villa Viscaya, South Beach, check out Jai Alai (not sure about the season), the Planetarium, etc. Have a great time!
I was booked at the Holiday Inn-Port of Miami, until I found out they only thing they offer is a bed. I found out that LaQuinta on Lejeune Avenue near the airport has a free airport shuttle that runs from 6am-11pm, free breakfast and a free shuttle to the Port! I checked their rates online and called the hotel. The cheapest rate online was $94.00 a night. I called the hotel back and told them of the internet rate and they gave me the internet rate. Good Luck