The Keys are nice; my brother did a swamp buggy ride somewhere near Orlando; St Augustine is, I believe, quite attractive, and claims to be the oldest city in the US. I think there should be plenty to do in Miami (we people watched while dining at South Beach). Basically, there’s a lot more to Florida than Disney. I would look into things like the last few drive in cinemas, go to sports events (we’ve only been in October, to catch the hockey season) etc Your accommodation provider will probably have loads of info.
It’s interesting to get off the beaten track – just hang around the Orlando parks and it’s easy to forget that you’re in the South. We took minor roads from Orlando to Miami, which took us through orange plantations and a town with one of the highest murder rates in the country – in some places there was a stark contrast between the houses, and the divide is still largely on skin colour!