Bern's is definitely at the top of the list. You are going as much for the experience as for the food, which is really, really good. Great steaks, an AMAZING wine cellar, vegetables from their own garden and a wait staff that has to apprentice just to work there. Don't skip the dessert room. Oh for the days when you could smoke a cigar in there.
Ybor City is a must for any cigar-lover. Tampa Sweethearts is a definite stop you will want to make. You can probably expect to see Fuente, Jr. in the store. Just keep in mind that it is not a typical retail shop but really just a small frontage for their mail order store. Still, worth the trip. And while you are in Ybor, stroll through 7th street, visit the other cigar shops (some likely to have rollers working) and stop by the Columbia Restaurant for lunch. Do all of this during the day, 7th Ave is blocked off and turns into a street long bar in the evenings.
If you are in the mood for a little gambling (what passes for slots here, table games and poker), the Seminole Hard Rock Hotel & Casino is a nice place, though you can find a good card game in any of the race tracks around as well.
Bush Gardens is of course worth a visit if you are into the theme park scene. Mostly rides and some good animal attractions. I have a friend who works there, so if you go let me know ahead of time and I'll see if I can get any behind the scenes stuff set up (no guarantees).
Clearwater and St. Petersburg Beach are not in Tampa of course, but it's a short drive and there are some great restaurants in that area. Frenchy's Rockaway Grille on Clearwater beach is an amazing place to watch the sunset and enjoy some great Grouper and/or she-crab soup. Salt Rock Grille on Indian Shores and The Lobster Pot in Reddington Beach (South of Clearwater Beach and North of St Petersburg) is also amazing, but really there are a TON to choose from. It is also worth a ride on the Sea Screamer to watch the Dolphins jump in the wake. They do a good job of tour guide as well.
Hyde Park and SoHo in downtown tampa are both good eating and night spots.
If you are into golf of course there are TONS of courses in the area. Let me know what you are looking to get out of the trip and I'll see if I can be a little more targeted in my suggestions. Also hit me up if you want to share a smoke while here.