I am also lookinf for a place to stay in Miami. We are cruising on the Liberty OTS in November.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Vision OTS 2-14-2015
Bid 4* on the Miami Downtown area: Start at $75 and you will probably get: The Hyatt, Radisson or Marriott.
Go to Biddingfortravel.com for some great information on how to bid.
I have stayed at each of these hotels, plus the Intercontinental, and they are all nice hotels and less than a $10 cab ride to the port. The Radisson, Marriott and Intercontinental all have port view rooms.
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I've stayed at the Marriott (careful, as the hotel, when we were there last Feb was not well marked-- some other name out front, and difficult for friends to find). It is across the road from the port entrance, but then it's a longer road to the ship, so the cab will still run $10 -- skip the vans, get a cab, as the vans will charge you more as they do pp). There is a very nice outdoor canal front restaurant a short half block away, and a Walgreen's across the street for last minute needs. I found the hotel very nice.
Last year we stayed at LaQuinta Miami Airport East. They picked us up at the airport, and had a free shuttle to the port the next day. There is a restaurant just a walk across the parking lot. Light breakfast in the morning. Very clean and nice rooms. Great staff. But make sure you book the correct LaQuinta as there is at least one more LaQuinta at the airport.