There are bars with televisions that show sports, right? Is there a bar that might be streaming Rolex coverage? If not... is there maybe a bar owner somewhere who is also a horse person, who might be persuaded to make an event of the event? I don't have a TV and can watch on my computer, but it would be fun to go somewhere to watch with others.
Maybe Satisfaction's? It depends on what other sporting events are going on then, I suppose, but Satis has a bunch of TV's and in the daytime I'd imagine they'd change the channel for you. If not, you could walk across the street to Alivias or Devines and try them. A little college-y at night (I'm at Duke) but i'd imagine during the day its fine!