We booked the Sheraton for $90 off of Priceline. Never did it that way ever before - where you name your price -- so can not complain. I was very nervous doing it and expecting something really bad but am satisfied. The cheaped I saw the room rates just today is $149 on 7/31 for us at the same hotel.
Try it out. You give the vicinity and star grade level you are willing to accept and then put a dollar amount out there. So as a heads up 3 1/2 star level with 90.00 bid - you just may be able to go lower.
Don't forget the port and airport are all in close proximity to each other which makes it a great place to port out of.
I'd suggest most any hotel in the Westshore area. Very close to the airport, and probably offer complimentary limo to the hotel from the airport, and lots of good restaurants, and shopping in the area as well. As noted above, the airport and port aren't all that far apart, so most any hotel in between is a plus.
Hope you have a GREAT time in our city,,,I know you'll enjoy the cruise!