If you have a vehicle, I suggest driving to St. Pete and walk along Bayshore Drive and visit the pier and Vinoy Resort.
If staying in downtown, then the Florida Aquarium is nice. There is also the river walk and a few places to eat near the convention center. Ybor is nice to visit during the daytime for a small bit, but the Columbia restaurant is a must try (the salad is excellent). There is also a trolley station there (next to the parking garage) that can take you to downtown Tampa and back.
There are some really nice gems of eateries scattered around the area; I only found them since my friends live in the area for a long time and shared them with me. They are no frills, but authentic Cuban style food.