I'm in the Tampa Bay area and agree that it has a lot of what you are looking for. Your desired acreage and price point might be a little harder to come by right now, but may still be possible (maybe the rural Bradenton area?).
Schools here are kinda meh, but not terrible. There are some great (by Florida standards) magnets to choose from, and both of my kids are products of the Pinellas County public school system. Schools offer all the usual options for Gifted, Honors, AP classes, IB, etc., so I wouldn't write them off completely. I have found that teachers and administrators are very willing to work with the kids and parents who want to succeed. Both of my kids have had some amazing teachers over the years! Florida also has the Bright Futures scholarship program (although it is currently being debated in Tallahassee) for high-achieving students. My oldest kid is currently attending UCF on a full scholarship, thanks to that program. That's huge!
For biking, we have the Pinellas Trail (and several others), a rail-to-trail project that goes from Clearwater to Tarpon Springs, and other projects/plans for possible extensions. You can access beaches, breweries, awesome downtown areas (Dunedin, St. Pete, etc.) and other cool stuff from the trail. A couple parts of the Trail are a little sketchy, traffic- and neighborhood-wise, but overall it's a great, safe, and well-used biking option. Beyond the bike trails, some parts of Tampa Bay are relatively bike friendly, but most aren't. Florida drivers fully deserve their reputation around here!
Sorry, I feel like I am writing a brochure for the Chamber of Commerce. :) I've been here for 25 years (I'm a Yankee), and the area has really come into its own in that time. Climate change is a concern, of course, but if you're not buying a multi-million-dollar home on the beach, you're probably good for a while. And, as someone else said, you know when the hurricanes are coming, and you evacuate when in doubt. I used to be more comfortable riding out the storms (block construction, non-flood zone), but now we err on the side of caution. Hurricane Irma was a wake-up call.