There isn't any sightseeing at the airport.
If you are arriving by afternoon, you are better off staying downtown. If you are only looking for a bed, then the airport is cheaper.
Problem is with your cruise leaving out of Ballentyne. IF you stay downtown, then you would leave your bags with your hotel bellman, and do your sightseeing until you board your ship.
If you stay at the airport, you'll cab to the port, then have to cab back and forth downtown, or make your touring arrangements, somehow. Ballentyne is in an industrial area, nothing worth seeing.
Priceline may be your best option?? The Days Inn, although basic, is an excellent location.