The only time you'll go "all over the state of Florida" is if you choose to do so. I have a friend who chose to go to Australia, California, Miami and other places-- but that was his choice. I chose to do a couple of away rotations in third year, but I purposely chose places that had free food and housing-- many of them do.
If you choose to live in Bradenton, though, you may have to do cores and electives in more than one place but you certainly don't have to go some place you don't want to go.