I always have went during the first week of March due to my college Spring Break being in March. Many colleges in Florida have there Spring Break in March, so keep that in mind. However, my family and I have a very low tolerance for crowds. That being said, the crowds during the first week of March have not been not crazy at all. Great weather, lower crowds, first week of March is an awesome time to go!
Disney offers a sort of "Spring Break" kind of deal. I book very last minute being an AP. So I, myself, notice this deal in like January.