You got tons of suggestions already to keep you busy in Tampa, especially if you're doing any diving/snorkeling, but if you're not doing these things and also are more interested in touring the gulf beaches...you could go to Fort Desoto (amazing/quiet and seculded...can google it...) drive up Gulf Blvd all the way up to Clearwater beach (~1 hr)...stop for awesome seafood along the way at one of dozens of good restaurants...that will be a stop/tour of a more quant/secluded run than Clearwater beach.
That said...Clearwater beach is more of a young (hot bod etc) scene than the St. Pete Beaches...so pick your poison...relax and soak up the sun or people watch.
If you do that tour, you could hit St John's Pass in Madiera Beach, boardwalk with shops and restaurants.
I lived on a key 5 minutes from Ft Desoto