I lived in Tampa for about a year a few years ago, and still go back a few times a year. As I’m sure you already have heard, Ybor City is the “hottest” place to be. It is a great place, but go on thursdays so that you don’t have to fight the amateurs on the weekend. There are so many clubs there (like a mini Bourbon St.) just try 'em all and see what fits.
As far as gyms, if you stay by campus, you are not going to get anything more than a big room with some weights, usually OLD weights. Not that that is a bad thing, but they usually lack any of the latest or quality cardio equip. However, most will give you a year for under 2 bills, so value-wise, it’s great.
Get out and explore, Tampa and St. Pete/Clearwater have a ton of stuff to do. The beach in Clearwater is one of the best in the country, huge, white, clean, and loaded with girls. Park at the Surfside for $20, get some drinks at the bar and head to the beach.
…and if you have the coin, Tampa sports one of the best restaurants in the world, Bern’s Steakhouse. Among other things, it boasts the world’s largest wine list, coming in at just about 6,000 bottles, and a stock of over 700,000 total bottles. They age their own beef, grow their own veggies, and make everything both on and off the menu. After dinner head upstairs to the dessert room, your private room to enjoy over 100 ports by the glass, and every type of dessert you can imagine (I strongly suggest the Bananas Foster). Just make sure it is your cheat day