If you are entering Keeneland from the main entrance (on Versailles Rd) drive until you reach the clubhouse and bear to the right around it. You will immediately see rows of parked cars beneath the trees and you can park anywhere there in the mornings.
If you come in through the entrance at the intersection of Versailles Rd and Man O' War just drive until you see the grandstand ahead of you at the top of the hill (at that point barns 1-6 will be on your right.) Again, look for the rows of parked cars. In the mornings, there are plenty of spaces available.
You're welcome! There's tons of room in the mornings. As long as you stay out of the spaces that are marked with trainers' names, or say Vet, or Press, and you don't park in the members' lot (to the left of the clubhouse) you're pretty much fine anywhere.