I would need a little more information to give a great answer. However, with what you're telling us, I would say it likely couldn't hurt (usually). Most of this can be generalized to whatever region people want to apply. I came from Texas and interviewed all over, so I faced this question many times.
What PDs are looking for is the answer to the question: "Why do you want to come to x? And are you serious about relocating your self, your family, etc., and will you be happy here? If all your family is here and you spend a lot of time here, but you ended up going to a NE med school and now want to come back, that's an easy question to answer.
An away rotation shows a program that not only are you interested in the program, but also interested enough in the region to spend a month or so "checking it out." Away rotations are a two edged sword however. If you go to a place, work your butt off, and look like a rock star, they're going to help you. However, if you go to a place and don't stand out from the crowd, are lazy, not interested in getting to know the residents, etc - they could actually hurt you. If you are marginal on paper, however, I think the chances are better that it would help you. Programs are more likely to "take a chance" on a person who is marginal on paper, but whom they really liked in person.
The other thing is that getting a SLOR from one of the Florida schools (or whatever region you want to be) might carry a little more weight with some of the regional program directors because they are likely to know each other and speak on a fairly regular basis.
