To me, Tampa means Cuban food! I lived in Tampa for five years and got my undergrad degree there. While most students around the USA live on pizza and burgers, I got through college on black bean soup, yellow rice and delicious grilled fish.
An institution of Tampa is an ever-expanding (takes up almost a whole city block now) diner/restaurant named La Teresita. This restaurant is not located downtown and is off the tourist beat but well worth the visit. No ambiance, mediocre waitstaff but food to die for.
http://cuban-food-usa.com/tampa_teresita.html