Colorado
Outside of the obvious, the beautiful Rockies, which are at their best in winter...
I'd recommend if you're going north to I-90, take I-25 to get to Sheridan and Billings...it's scenic and faster than taking I-80 and going through Utah and Idaho. Also, if you're going south, I-25 goes all the way down to El Paso. And if you can time it right, stay at the Motel 6 in Casper WY, at the Poplar Street exit. It's right across from Banjo Bob's Barbecue, which has the best ribs, the best chipotle barbecue sauce in the universe.
Likewise, if you can time it right again, take your night's stay at the La Quinta in Colorado Springs, at the Garden of the Gods exit, which has, right behind it, Antonio's, which has one of the best chicken piccatas going.
Colorado is a crossroads to everywhere. If you're going to pick up I-40 in Amarillo after you cross the border into NM, you may want to take the side route vias Raton Pass and over to Clayton and on via various small towns to Amarillo. It's a good shortcut. It's two-lane with intermittent passing-lanes, so if you're behind a truck, don't despair and don't risk your neck. You'll get your chance.
Also, out of Colorado, you can cut across Kansas out of Denver, to tie onto another main east-west highway---I-70, maybe.
Denver traffic: you will want to time it to go through Denver at a non-rush-hour, believe me---having nearly been hit by a confused house-mover in a rainy evening rush: the traffic is very heavy, and the heavy traffic period is very long. Rainstorms are frequent. And I-25 besides bearing city commuter traffic carries all commercial N-S traffic in this end of the US. Bypasses are scarce and difficult to get onto. If you don't stay for the night north of Denver, the next best opportunity for a hotel is at Colorado Springs. We recommend the La Quinta, especially if you're traveling with pets. There's also a nice(and pricier) Holiday Inn on the other side of the highway.
What to visit, now, inside Colorado and off the major highways, is a wonderful choice: many of the small towns are as easy as Denver is frenetic, and very walkable, with lots of from-the-road views as well.
The Colorado Monument: a wonderful preview of Arizona's Grand Canyon. This is right outside Fruita, Colorado, which has a marvelous dino animatronics museum and a nice little gift shop, with a hotel right across the parking lot. Food, in Fruita, is decent: we had a nice supper at a Mexican restaurant on the easy-going main drag. It's easy to get there and back to the hotel area if you have any bump of direction at all. You go over the bridge to get to food and over the bridge to get back to the hotels.
I'd also recommend Manitou Springs, a very new agey sort of little town with amazingly picturesque streets, lots of artists, and some pueblo ruins. I don't have any pictures of it, alas. My battery was out.
Then the Black Canyon of the Gunnison, another place where the tremendous Colorado plateau uplift, which created the Grand Canyon, has let rivers cut down through interesting rock layers. An interesting fact: the only spot on earth where there's a greater plateau, I am told, is the Tibetan Plateau, near the Himalayas. Geological history here is fascinating. I recommend The Roadside Geology of Colorado, a wonderfully readable and abundantly illustrated book, for your driving partner to read aloud as you travel. Often when you comment, "Look at those weird rocks!" the book will have an exact picture of the oddity and an explanation of how it got there. The whole book is keyed to highways and routes.
The Black Canyon.
Another beautiful sandstone formation, due to that violent mountainbuilding, is that of Garden of the Gods, near Pikes Peak, at Colorado Springs. It's an easy paved walk among the spires, and a wonderful camera fest.
There are very many of these: they're old alluvial fans, so the book says, tilted on end, from the time when the Colorado mountains were islands in a primaeval sea.
Aside from all that, on the other side of the Front Range, is the curious Great Sand Dunes National Monument: all the sand from the erosion of sandstone in the mountains comes here, by a fluke of the wind. A river runs through it. Or underneath it---depending on how the sand is lying that day. When the river is out, it's nicely wadable.
The first time I was there, the sand had mostly covered the water...which is what brings it. But on this day, and, to look at those trees, recently, the river has been quite present.
Considerably north of there, and a little inconvenient unless you're going up to Fruita, is Dinosaur National Monument, over near Utah: this is the bonebed from which many of the dinos in famous eastern museums were taken. Visitors can see firsthand whence such specimans come, and if you're from the eastern states, you may recognize the home of an old museum friend.
Also, if you go to see Flaming Gorge, quite a lovely trip around that area---go the eastern side of the reservoir, in order to see the really pretty rock formations. We made it on the proper side our first trip, where there was a beautiful drive through red sandstone, and were disappointed on our second trip when we accidentally missed our turn and went on the wrong side of the lake. By then we were too far to turn around and make it to a reasonable stop that night.
Also---when in this area, stay at the Rodeway Inn in Vernal, Utah. The floral baskets are amazing: it's also nice and inexpensive.