The French Laundry is one of those places that you have to plan to go to in advance, two months in advance, more specifically :P  You could check OpenTable for cancellations daily, and one thing that you might want to try is calling them and asking their reservationist (that's what FL calls it) to let you know if there happens to be a cancellation on that day.  Chances are slim since they do have a hefty cancellation, but it does happen.

And if it doesn't, lucky for you, there are a ton of other great restaurants on Washington Street where FL is located, including two other Thomas Keller restaurant -- ad hoc and Bouchon .  Those are two restaurants that you'll still need reservations for, but it's much easier to get reservations there as they're more casual spots and less time-consuming to dine at.

Here are some other really good ones:

• Bottega -- Italian restaurant owned by a Top Chef, as in the show!  Enough said.
• Redd -- Good American food and the restaurant decor has a more modern touch compared to other places on the street
• Bistro Jeanty -- Awesome French restaurant
• étoile Restaurant -- This one's actually at the lovely Domaine Chandon not too far off Washington St.  Yet another great French restaurant.  Do the tasting menu

Those are half a dozen of the creme de le creme of Yountville dinner spots.  Good luck choosing a place!

The French Laundry?  Fancy!  I'm sorry that you couldn't get a reservation there.  If you want to go somewhere really nice, I have one other suggestion -- It's not in Yountville proper, but it's in Napa which is plenty close -- Morimoto.  It's some of the most amazing Japanese food I've ever had and as you know, his name is just about as recognizable in the culinary world as Thomas Keller's is.