Since it's post cruise and you will be off the ship early, I would suggest the Brickell area. There are plenty of things to do, things to walk to and lots of restaurants. It's close to the port as you know and a short ride to the airport. I wouldn't suggest staying near the airport because there is nothing to do out there.
Hampton inn Brickell is a great hotel as others have suggested and there are plenty of others in the immediate area that are also fantastic. Hotels that have great pools as well. It will all depend on what price point you want to stay at since you can go from the prices of the Mandarin Oriental and Four Seasons to much lower.