My grandfather (who I never got to meet, but I hear was totally awesome) went to the University of Tampa. The most distinct thing about the University is its minarets . . . . those onion-looking things that look like that where plucked right out of Red Square that are on top of the oldest part of the university. You can see them when driving about downtown, but I'd stop in for a closer look. The university also houses the Henry B. Plant Museum.
If you are wondering downtown you will probably notice a group of buildings resembling the Kremlin in Moscow. This is the University of Tampa. Originally the Tampa Hotel it was turned into a University and sits along the Hillsborough River.