I don't know whether drone flight is permitted there, but a visit to the Shaker Village at Pleasant Hill should be a priority. It's located about 25 miles SW of Lexington on the road to Harrodsburg. A large acreage with many elegantly restored buildings and furnishings. Lunch at the Trustee's office is a must. I've visited the more well-known Hancock Shaker Village in western Massachusetts, and this attraction is much better.
A visit to the college town of Berea, about an hour south of Lexington, is also worthwhile. It's known for a thriving and highly regarded crafts scene.
Google both for more information.