Back in 2003 I graduated with a degree in Information Systems from college. The company I was working for at the time offered me the I.T. director job if I was willing to relocate to the Tampa area. I jumped on it and spent 2 years down there and enjoyed it a lot. Good luck finding something but I agree that the best option would be to stay with IBM or a subsidiary. Definitely find the job before moving.
On a totally different note, make sure you really think about what living in Florida entails before moving there. I'm not trying to say you won't like it but living there is a much much different experience than going there for a week at a time. The insurance is ridiculous, the traffic bipolar, and the humidity pretty bad. It may not seem so bad when you are walking around in flipflops on vacation but try getting in that hot car or walking from the parking lot into work in a suit with it is 90 degrees with 100% humidity.
I would spend some time talking to people who relocated there and make sure that the FL living experience is what you are looking for.