I have always thought that the area around Lexington enjoys the best climate in the state. It has a ring of hills around it which break up weather patterns (tornadoes, cold fronts, etc.), sending them up the Ohio River.
You should know, though, that central Kentucky has a LOT of rain and heavy cloud cover, at least 5 months a year. Coming from southern California, you may find it oppressive. Seriously.
On the other hand, you might love it. Only you can say.
Kentucky homeschooling laws are some of the best in the nation.
You can easily find a lovely home for WELL under $300k.
Look at London too.
Around Lexington, the small towns I can recommend are: Versailles, Midway, Wilmore, Paris, Berea, Danville.
Elizabethtown, Bloomfield, Shelbyville are a little further west, and have a good bit to recommend them.
You might actually look in Franklin County and/or Owen County. Frankfort is the state capital, and there is a lot of absolutely beautiful countryside throughout the area. Really gorgeous rolling hills and valleys.
The whole state is MUCH prettier after April. If you go to look at it, wait until spring so you can truly appreciate it.