The Ringling museum of art is very, very cool! No it is not clown paintings, but real works of art. It is just off of 41 SW of the airport.
http://www.ringling.org/
There is also the Ringling House there called the Ca' d'zan. It is a beautiful house that has been restored to its former glories.
If you are still into art head up into St. Pete and see the Salvador Dali museum, also incredibly cool.
You can head south to Venice and go snorkeling ofr sharks teeth at the beach.
Head east to Arcadia for some antique shopping
Or head to the north and go canoeing on the Hillsborough River.
http://www.canoeescape.com/
These guys will outfit you, drop you off and then pick you up after the trip. I have done several tours with them and the river is great and you will have a ton of fun.
For dinner head up to Bradenton/Ellenton and go to the Crab Trap II at Manatee and I70.