If you’re into show jumping history or hunter/jumpers and go to the KHP on a weekday during the USHJA office hours, you can visit the Wheeler Museum (which features tons of way cool historic hunter/jumper items on display - current exhibit I believe is still horse show photography themed and features really cool photos through the decades including a section of Budd Photos that I don’t think have been seen a lot) it’s a small museum, and the hours are funky (weekdays only, though in the past I think they’ve sometimes had special hours around events like LRK3DE/Rolex and so on) b/c it’s in the USHJA’s offices but if you’re there on a weekday between about 9 and 5 stop in and check it out. I’ve always thought it was a bit of a hidden gem. Also, all the show jumping HoF plaques are displayed in the area below the bleachers for Rolex Stadium and that’s worth at least a walk-through.
I’d also second the TB Farm tours if those are still an option, there’s a lot of buses and stuff you can coordinate with a KHP visit, and if you can, also, while at the KHP check out the Hall of Champions - you’ll get to see the famous horses in residence at the park including Funny Cide.
Personally, the International Museum of the Horse is great for like, a one-time visit to say you’ve seen it, but I think it’s a tad overrated, they don’t really change up the displays or anything.
Keeneland - this just reminds me someday I’d like to get to Keeneland again, I’ve been once and it was fun but I went on a day they were running a G3 stakes so it was pretty busy and I felt like I didn’t have as much fun as I might’ve on a more low-key day. (I like to take pictures of the races and watch from right on the rail when I can, so.)
Sorry, no recs on places to eat, every time I’m in Lexington I either get food in Indiana (live in Indiana, approx. 2 1/2 hours from Lexington) on the way home, or I seem to inevitably wind up at the nearest Cracker Barrel.