The TCC has a parking garage that is located across the street from the building. It's five dollars a day and I believe it fills up pretty quickly - but I don't have a good gauge of when exactly since I park there Thursday morning and leave Monday afternoon. XD
<-- Here's a parking map for downtown Tampa, for reference. I know my GPS takes me downtown to where there are signs for parking, so I'm not completely certain about giving good directions... But there is a parking garage, and some nearby alternatives for when the TCC garage fills up.