Don't forget the Double Six
Depending upon how much time you have, get off the interstate, and get on Route 66 which will be running alongside the interstate on I-40.
Check out the Big Texan, home of the original free 72 ounce free steak (if you can eat in in one sitting) in Amarillo and Cadillac Ranch to the west of it. At the Texas-NM border, visit the ghost town of Glen Rio, but you can't stay at the Last Motel in Texas anymore. You can see first-hand what the interstate can do to a small town.
Once in New Mexico, its "Tucaumcari Tonight". Check out the Rt 66 statue of the tailfins and buy some curios/souvenirs at the Tee Pee.
http://www.roadtripamerica.com/blueswallow190.jpgThere are many motels, but if they let dogs stay, you definitely want to spend the night at the Blue Swallow Motel. It has just reopened and has been restored to its former glory. It's an experience you won't forget and you'll love that great old neon sign.
RoadDog "Keep on Down that Twolane Highway."