Hmmm.... There are lots of good hotels near the Miami cruise port. We've stayed at the Marriott Biscayne Bay before and enjoyed it. However, it is not "on the beach" for which you would probably need to look into Miami Beach hotels. Be aware that anything you find there will be very, very $$$$$.
As far as getting to the cruise port on the day your cruise leaves, I'd go with several Taxi/Uber/Lyft vehicles. However, you may find that your hotel will offer transportation (for a price) and that may work out better for you.
