I often get asked from people out of town, where is a great location to take photos that is outdoors when I graduated from another school.
University Of Tampa is one of the best locations for this. I spoke about using this area before for photos but the campus has great location for non UT Graduates here as well. I have shot graduates of FAU, FSU, USF, and ect here and really utilized the campus to it's best while here.
For parking, make sure to utilize the free parking by the library or by the parking garage off of Kennedy blvd. I'm not sure of how they handle parking violations but I sure would not like to find out either.