Welcome to Tampa!
The Florida Aquarium (next door to the cruise terminal) will store your luggage while you visit the Aquarium (small fee for the aquarium). There are also museums down town. Next to the Carnival cruise terminal is an old battle ship that people take tours on (for a small fee) if you are interested in history. If you have a rental car you might want to drive across one of the bridges to St. Petersburg or Clearwater and see the beaches.
Just make sure you are at the airport at least an hour before departure. The traffic between 7:30 - 8:00 a.m. and 4:00 p.m. - 6:00 p.m. is bad if you are on any of the major highways.
To bad you don't have a couple of days; there is a lot to see in the Tampa Bay area. My family loves Busch Gardens (it takes all day) and the cost is around $60.00 per person. We have Florida residence rates so I'm not sure what the rate is if you are from out of town. They have a web page at www.buschgardens.com
and you click on Tampa, if you want to see what Busch Gardens is like.
Feel free to ask me anything and if I don't know the answer I'll check around for you. I'm a Florida native.