I would highly, highly recommend a trip to WinStar Farm. You can definitely schedule an appointment to see their stallion barn. They tend to keep the mares and foals off-limits, but the stallion barn is definitely a treat in itself.
I had the great pleasure of having a complete farm tour last year, including the training barn, broodmares, and, my favorite, meeting Tiznow, Distorted Humor, Harlan's Holiday and Super Saver. Tiznow was a real puppy dog and mugged for mints the whole time I was standing there with him (of course, with his groom standing right there too :))