There are several options for you to choose from:
Rent a car for the day.
Use Public Transportation.
From there many folks will opt for a day at one of the following places:
South Beach(easy with public transport)
Down Town Miami(easy with public transport)
Everglades(best with a rental car)
As for your bags, some airlines will check your bags from the Cruise Port(for a fee, check with your airline)
If your airline doesnt offer that service you could head to the airport and check your bags in early( may depend on the local ticket counter being open)
you could store your bags at the airport(fee applys)
Depending on your destination some Hotels store bags.
Pick a spot and a mode of transportation and some idea of your dates of travel/budget and then we can offer more suggestions from there...