When I say you have to request the tickets (for 2003) the day AFTER the derby (2002) I mean that almost literally! Before the Preakness. From what I understand they get a lot of requests and they fill fast. So this year, the day after the derby, write for tickets for next year.
About and hour and a half away is Lexington, where you can go see Man O'War's grave/statue at the Kentucky Horse Park!! As you know it doubles as a museum, but they sometimes house actual horses there. When I was there I saw Cigar and Da Hoss. I highly recommend it.