OP, are you travelling alone?

Here's my recommendations for time to kill:

1) El Puerto in Ybor is a really good hole in the wall Argentinian family owned restaurant. Their chimichurri sauce is off the wall amazing!! Is definitely a local's place to go.
http://www.elpuertoybor.com/

2) Cigar City Taproom is close by the airport. They have a lot of unique CC beers on tap and other things to do like shuffleboard.
http://cigarcitybrewing.com/tasting-room/

3) Downtown St Pete (DTSP) has a lot of great things going on right now. Can walk along the water front and relax. Plenty of cool shops and restaurants. Further inland is Urban Brew and BBQ. They cook their mac and cheese in a skillet and is to die for. The Birchwood also has a really nice rooftop bar that overlooks the waterfront park.
http://www.ilovetheburg.com/

4) Mazzaro's Italian Market is unique to St Pete and has an awesome wine and cheese room. The chicken parm sandwiches are the best. Mazzaro's is closed on Sunday's though.
http://www.mazzarosmarket.com/