There is parking directly at the port of Miami which is safe and secure. Cost, I believe, is $10 a day (payable upfront).
While in Nassau you can:
--Head to Paradise Island via water taxi or cab to check out Atlantis and Paradise Island Beach
--Spend the day at Cable Beach
--Visit Stingray City, or swim with the dolphins
--Do some duty free shopping
--Take a catamaran snorkeling trip (Rose Island is great) or SNUBA
These are just a few suggestions - No matter what you decide to do -You should have a great time - Enjoy!!