I don't consider "cities" and "good biking" a great fit. But I'll put a plug in for Olympia, WA... at least for May through October it's paradise.

1) Good public schools for our son Olympia School District
2) Great biking - great trails, bike lanes, and awesome country roads
3) Progressive, functional politics/city + state management - Olympia is a "government city"
4) Great scenery - views of the Puget Sound, Olympic Mountains, Mount Rainier, and lots of roads lined with large fir trees.
5) Great weather - 55 - 80 for May through October
6) Hot is good, cold would have to have awesome Springs & Summers - Sorry, can't provide the Hot. But summers are what people come here for.
7) Affordable cost of living - I'm guessing the same as Tampa
8) Friendly people - Absolutely... check out capitalbicyclingclug.org