We just stayed at the LaQuinta Inn on LeJeune Road. Free shuttle from the airport to the hotel and to the Port of Miami. There are two restaurants near by-Brennigans and a steak house in the Embassy Suites next door. Almost everyone at the hotel was leaving on their cruise the next day. I think it was $85 for the night, free shuttle from the airport to the hotel, from the airport to the Port of Miami and a delicious breakfast. We would definitely stay there again.
I saw someone else mentioned the Holiday Inn by Bayside. We went to Bayside in the evening and saw the Holiday Inn across the street. The street is 6 lanes, but has a cross walk so it is easy to get to it from your hotel. The hotel is close to the Port Of Miami, I'm not sure if they have a shuttle service or not. I know there were a couple hotels that offered cruise packages that included shuttle service from the hotel to the port.