Florida, off the beaten path?

Ok, I'm flying to Miami next week. My questions are not about Miami itself instead about places around Miami (and the rest of Florida) that are NOT-TO-MISS.

I know about the Keys, Everglades, and Theme parks, but I'd like to hear reports from people who've been to other places (less commercial, less touristy places) (i.e. cities, towns, neighbourhoods, national/state parks, beaches, lookout points, and other natural or even architectural highlights) in the state of Florida.

Time is not an issue, but money is.

So what do you recommend that you've ACTUALLY been to and can vouch for?

Thx in advance...