Get tickets and join the fans at a game at Alumni Memorial Field. If there's nothing on while you're there, you might like to check if they give a guided tour of the facilities.
You'll soon learn why this Lexington sporting facility is visited by many travelers. If you're looking for more to explore, Washington and Lee University, Virginia Military Institute, and Virginia Horse Center are in the area as well. They won't take long to get to from Alumni Memorial Field.