A google map showing UK and Lexington destinations:

The most convenient airport to fly into is the Lexington Bluegrass Aiport (LEX), which is a short 15 minute drive from the University and your hotel. For more flexibility, you may also consider Cincinnati (CVG) and Louisville (SDF), which are bigger airports and each about 1.25-1.5 hours away. The best way to get from CVG/SDF to Lexington is by rental car.