Roaches. Everywhere. Both the typical German Cockroach and the sometimes very large "Palmetto Bug" (a roach).
Chiggers, mosquitoes, and no-see-ums. I got bit up in DECEMBER. Imagine what summer is like.
In North Florida, geckos were quite numerous - even in houses. In South Florida, the number of legged reptiles is larger.
Termites, fire ants.
And gators are a possibility in or near ANY body of water, which, in Florida, means just about anywhere.
And you already mentioned the heat & humidity. It can get ungodly.
Weather-wise, it's hard to beat Cali. But a lot of people are getting fed up there with all the inconveniences.
My "if it was me" recommendation? What about the Norfolk/Virginia Beach/Newport News area of Virginia? Winters are *relatively* mild. Some palms grow unprotected (Sabals, Butias, Trachies, and the odd Washy & Med Fan). It's a nice region with some great neighborhoods.