This is a web site for Tampa Bay martial artists --
http://martial.meetup.com/18/members/. Information from this site current as of October 2004 --"Tampa Family Martial Arts, Goju Ryu. We have about 30 students. Anyone interested in working out, please call 813 317-7988."
The Kyokushin dojos in Zephyrhills and Brandon will require bus trips if you don't have a car. There's an Aikikai dojo within walking distance of UT that's good. Other dojos in the vicinity probably require a bike to get to and I don't know about their styles or quality of instruction.
If you've any interest in judo then try instruction with Professor Ed Maley. He teaches out of a YMCA approx 5 miles from UT (http://www.floridaschoolofjudo.com/schedule.html) from noon - 1 pm MWF.
A good Shuri Ryu dojo is run out of Lightning City Gymnastics (http://lightningcity.com/) by Sensei Luis Lugo, but this also requires a bus trip since it's in north Tampa.