Possibly Sarasota, FL? It's a little below Tampa. I know you mentioned you don't want the temp to go below 50 at night but what about oppressive heat? Is that a concern? In central FL, 6 months of the year, the weather is nice but the other 6 are very humid and hot. Some people don't mind that. When we lived there, it did not bother me that much. My husband hated it, hence the reason we are now living in SC. We are originally from PA and it's going from one extreme to the other. I hear you on the freezing cold weather up north. I hate cold! Depending on where you are in GA or SC, it will give you seasons and a better climate. Yes, it may get colder in the winter for a couple months, but nothing like Ohio, but the summer heat won't last as long as FL. Being in SC, we get cold days but it is definitely broken up with 60 degree and sunny days. It's Jan and February that are the colder months. As I said, I hate cold, but it's very tolerable to me. The rest of the year is nice. Just a thought.
That being said, I really enjoyed FL while we lived there for 13 years. You may also want to check out New Smyrna Beach or maybe Melbourne. If you live on the coast, you get the sea breeze. Your price range for a house in FL, maybe a bit of a challenge but it can be done. South FL will be ridiculously expensive.
Like someone else said, pick a city or two in each state and do some research on it. Once you narrow it down, try to visit the top pics. You can make your decision then
Good luck!
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I wish when people come here for advice, they come back with and update. 
