SECOND - I would definitely recommend that you take at a minimum a good half day while in Lexington area to visit the Kentucky Horse Park. It's a very good starting point for both those familiar with equines and those who are not. There may even be a special equine oriented event scheduled there during the time you are visiting but if not the Museum, the Parade of Breeds, the Audiovisual presentation - which is a great starting point - and just walking among the barns to take in the carriage collection, the beauty and peacefulness of this site - all these activities embody the spirit of the horse and Kentucky's long affiliation with everything equine. Not to mention that there are some very special retired Thoroughbreds residing there that you will want to visit. Also I *think* a really special Derby, horseracing trophy collection now resides there.
THIRD - We'd love to have you come visit Texas but it is at least a very LONG 1 day drive from Lexington to the northestern (closest point) of entry to our sprawling state. The good news is that if you want to check out the QHs many of the top farms are located in that NE area - in and around - especially the area north of - the Dallas/Ft. Worth Metroplex. Should you choose to come this way you could take in some horseracing at Lone Star (their TB meet is ongoing thru end of June) and also see Longhorn cattle driven to the Stockyards in Ft. Worth by cowboys on working QHs (it's a demonstration herd for tourists, the cattle are not destined for slaughter); maybe even find a local ranch horse competition to watch. Such competitions sponsored by AQHA are more focused on the equine-human partnership it takes to work a ranch: riding, team penning, obstacles trail, roping and reining competitions and general unflappable and versatile nature of the breed. However don't think you must come to Texas to see QHs - there are actually quite a few QH breeders in Kentucky and the state is on the brink of developing a QH track as I understand it so you should be able to find plenty of quality QHs to admire while enjoying Kentucky. I purchased a KY-bred QH filly several years ago at the Heritage Sale in Oklahoma City to train and race here in Texas. She was a decent enough 2YO who showed some promise but would have been better as a 3YO IMO but my partner wanted out so she is now a barrel racer.
Have FUN - and if you decide to drive an RV or car to Texas drop me a PM and I'll give you some more specific ideas of ranches to visit, contacts for them, etc.