April can be fantastic weather in FL, but it seems that spring break continues longer every year. I'd aim for the end of April and first week of May. The hours will be longer, the weather "warmer", but you'll miss the spring break crowd.
The first week in may is a really nice time to go. It's not too crowded and the weather is fantastic. It's one of our favorite tInes to go. I am trying to make it work for next year.