Blue Grass Airport (LEX) is six minutes from downtown by car. Most major US carriers serve it via Atlanta, Charlotte, Dallas, Detroit, and Chicago. The airport is right next to Keeneland Racetrack, which is sometimes also true in reverse — incoming flights pass over the racing oval.
By road Lexington sits at the intersection of I-64 (east-west) and I-75 (north-south). Louisville is 80 miles (1h 15m) west, Cincinnati 80 miles (1h 30m) north. There is no passenger rail service.