If you like abandoned buildings, you'll find a couple of old Williams Brothers gas stations along the way, as well as the famous Painted Desert Trading Post portrayed here:
http://images.google.com/imgres?imgurl= ... %26hl%3DenIf you REALLY like the trading post, you can buy it and the surrounding land -- I've seen a real estate ad online.
As for great burger places, I heartily recommend the Red Ball Cafe in Albuquerque. It's historic and located on Route 66 (4th Street just south of downtown).
My advice is to order the Wimpy Burger, which costs only about 99 cents and is small but not tiny ... and tell them to leave off the usual red chile and instead serve you both red and green chile on the side.
New Mexico is famous for chile (which usually comes in a form resembling salsa), and I have to admit I really liked the extra kick it gives food. You can even order a Green Chile Cheeseburger Pizza at the Pizza Hut in Grants, New Mexico.
But if it's a great burger you're looking for, the Red Ball Cafe served me the freshest, juiciest one I've had in recent memory -- like something off the grill.