Not to be a shill, but I fell in love with Lexington, KY after moving here a few years ago. Will go through your checklist and list the pro's and con's.
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Climate: All over the place. Spring and Fall are fantastic here. The local saying is "Don't like the weather today? Don't worry...it will be completely different tomorrow." and it's fairly accurate. This winter was a bad winter to judge, we had three 12"+ snow storms which is rare for this area. Summer hasn't been that bad this year (or the past few years really). The disadvantage is that it can get humid here at times, not nearly as bad as any coastal area but on an upper 90's day after a few days of rain it can be fairly unbearable.
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Affordability: It's pretty average, you're looking at $100 sq/ft if you're buying. Average listing price is around $270k, with the Median Sales Price sitting around $167k. Crime isn't much of an issue here unless you live in the downtown area surrounding the University of Kentucky campus. I lived downtown for two years and didn't have any issues personally, but if you turn on the news and there is crime being reported on, its either in the Louden Ave area (North Lexington, ghetto area), or near the UKY campus.
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Culture and Cuisine: Culture - Lexington is a somewhat progressive city due in large part to the University of Kentucky being located here. You'll likely find a 50-50 split of the local population being democrat/republican. Our Congressman (Andy Barr) is a Republican and largely useless (personal experiences from interacting with his staff). He ousted the 5-term Democrat Ben Chandler. So "culture" wise you'll hit every end of the spectrum here from the ultra-progressive to the ultra-conservative. History - Lots of history here, a pretty cool historic district. Lots of history with the various distilleries and early colonial history. Cleanliness - Pretty clean city, no air pollution to speak of. Does it get good music venues - Rupp Arena for some music, if you're looking for a fringe sort of venue you'd likely have to drive to Louisville (1 hour). Nightlife- Lots of local bars and clubs, as long as you don't mind college students. Cuisine - Lots of amazing restaurant heres. Malone's is one of the better steak houses I've been to. Their prime rib is the best I've had (St. Elmo's in Indianapolis has a far superior Ribeye though) Organic grocery stores/farmers markets - This is one of the major advantages of Lexington and one of the things I brag about the most. Lexington is a decent sized city that provides you with everything you'd need in a city, while being SURROUNDED by farm land. This means that we have not just a local farmers market that runs almost every day of the week (at different locations) but we also have a local supermarket co-op that sells local produce, meats, and the such.
Here's the link to that.
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Convenience: The only area you'll really find any form of "traffic" on is Nichollasville Road. It's the "main" road leading out of downtown towards South Lexington and towards the mall area. Starts out as a 4-lane, expands to six as you approach the mall. Shopping isn't an issue, there really isn't anything you can't find for sale. Lots of boutique shops around the downtown area and around the Historic districts just south of downtown. Walking anywhere is pretty much out of the question unless you live downtown (again, unless you're a student at UKY its not really recommended). There is a bus system, and plenty of taxi services (thanks to the large student population).
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Local Points of Interest: Since you're big on outdoor activities I think you'd love Red River Gorge, its 45 mins to an hours drive from Lexington depending on where you are. Its a wildly popular hiking area
here's a link including trail maps and some pictures. It's part of the Daniel Boone National Forest. A big tourist draw is the "Bourbon Trail" which is less of a "trail" and more of a fairly large collection of bourbon distilleries that surround the greater Lexington area. There are a few micro-breweries in the area that have been fairly successful. One of the major locations in the city would be Keeneland for horse racing. Being Kentucky, horse racing is wildly popular here. The area's just outside of the Lexington city limits are home to some of the most beautiful and perfectly groomed horse farms you'll see anywhere in the world.
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Nearby Points of Interest: Lexington is located smack dab in the middle of Kentucky, putting damn near any points of interest that you may find in the state within the three hour drive requirement you listed. You're an hour from Cincinnati and Louisville, and three hours from Knoxville and Nashville. You mentioned being close to family that lives in Virginia as well, depending on where in Virginia they are you could be anywhere from 6-10 hours driving distance.