Stuart is in the Treasure Coast region (basically Hobe Sound to Sebastian). In a lot of ways it is like Ft. Lauderdale from 50 yrs ago. I spend a lot of time there, on the water boating, nice little downtown, street festivals, restaurants, parks, etc.
Martin County has some fairly strict growth plans, which makes it a nice place to live. Only real downside is that housing has rebounded to near peak levels from before the bust.
If schools are your thing, Florida isn't the place to be, neither is Atlanta.
Wife and I had a chance at Florida before the last job and passed on it because Florida is one of those states the first thing they cut is education. Georgia isn't any better.
Good luck on your final decision.
FWIW The Keys, thanks to some generous donations from a local resident, has some decent schools.
You also mentioned Lincoln, NE as one location.
I can tell you from experience, I would avoid it. On paper it looks good. Decent schools, Balanced state budget, cheap costs to live, and it was listed at the top of list. The problem is everything that they listed as being good are not things the normal people actually spend time doing. It's basically the University of Nebraska and that is it.
There is not a lot there either if you decide on a career move.
An Ex-Nebraskan enjoying the heck out of life in Texas.