Well, let's see... quite a few things, especially if you don't mind getting off of the interstate a few miles here & there.
If you wanna try out your binge eating skills, Amarillo, TX is the home of the BIG TEXAN steak house, conveniently located just on the north side of the highway. If you're feeling brave, order up their 72 oz. steak challenge... and if you eat it all (plus the sides) in an hour, it's free.
Also in Amarillo... on the service road running parallel to the eastbound I-40 lanes... is the famous "Cadillac Ranch".
Moving along, I-40 through NM is pretty void of anything spectacular, although the scenery is very nice in places.
After passing through Albuquerque though, you have a choice of 2 places you can wander off and see if you like:
If you head south on I-25, and then west on US-60, you'll pass right by the Very Large Array... the huge radio telescope complex that is seen in the movie "Contact" with Jodie Foster. You can't go into the facility (at least, you couldn't a few years ago), but you can easily see the antenna farm.
Or, you head northwest out of Albuquerque via any number of ways and head up towards "Four Corners"... the geological spot where the 4 states of Arizona, Utah, Colorado, and New Mexico abut each other. Standing on the US Geological Survey market, you can say you've been in 4 states at the same time.
If you do head up that way... instead of heading back south to I-40, you'll want to continue west about 30 miles or so to visit Monument Valley, right on the AZ-UT border. This is the area where many of John Ford & John Wayne and other cavalry & western movies were filmed. Fort Apache, She Wore a Yellow Ribbon, and others. Truly beautiful landscapes. Also where they filmed the scene in Forrest Gump where he decides he tired, and going to stop running.
Well, If you stayed on I-40... or if you're heading back south to rejoin I-40... the interstate passes through the Petrified Forest Nat'l Park just east of Holbrook, AZ.
Continuing west on I-40, you go thru the town of Winslow, AZ... which any fan of the Eagles will know is where he was 'standin on a corner'. You can also have your picture taken there too. In fact, so many people do, they've made a nice place for you stand:
Just a few miles west of town, you'll find Meteor Crater... which is exactly what the name implies. Almost a mile across, and over 500' deep, it's pretty impressive.
Continuing west on I-40... about 30 miles on the other side of Flagstaff, AZ, you'll come to the town of Williams. There's nothing really impressive about Williams, except for the fact that it's where you turn off of I-40 and head north about 45 miles... where you reach the south rim of the Grand Canyon. I don't think I need to post a photo or say a lot about that except... you're so close, you can't just pass by and not visit.
Finally, continuing west on I-40... when you get to the town of Seligman, you can venture a bit north off of I-40 and ride the longest preserved portion of the original Route 66 all the way into Kingman. Just shy of 90 miles in length, it's a very scenic ride... complete with the old roadside Burma-Shave poem-advertisements about every 5 miles or so. And it takes you right back to I-40 in Kingman.
Ok, so that's about it from me. There are other nice things to see along the way, but those are some of the highlights.