Things to see in both directions
If you go toward Denver, you could include Lincoln County NM (for either direction, actually), Santa Fe/Taos and Eagle Nest, the Cumbres & Toltec Scenic RR at Chama, NM, Chaco Canyon, Mesa Verde NP, Durango (the DSNG RR is there also), Black Canyon NP, the hot springs around Glenwood Spgs, and some of the ski areas (in summer there's LOTS of possibilities for hiking), Garden of the Gods and Pikes Peak (Colorado Springs). In the other corner of the state (NW) there's Dinosaur Natl Mon, and near Denver itself Rocky Mountain Natl Park.
Toward Las Vegas, see some combination of the Silver City NM area, Fort Bowie (AZ), the Chiricahua Natl Mon and mountains, Bisbee, Tombstone (tawdry but fun), Tumacacori Mission, San Xavier Mission, Prescott/Jerome/Sedona, Oak Creek Canyon, Flagstaff (many attractions), Sunset Crater, Wupatki Ntl Mon, Canyon de Chelly, Hubbell Trading Post (Ganado, AZ), Meteor Crater, Grand Canyon, Monument Valley, Navajo Natl Mon, and the southern Utah parks (Zion, Bryce, Capitol Reef, Arches, Canyonlands, Cedar Breaks).
Maybe you can't see all of these sites, but you could choose the ones that interest you and plan a route accordingly. If you're not familiar with some of the places I mentioned, post again and I'll explain further.
Finally, the scenery on either one of these routes is alone worth the trip -- everything from low desert, high desert, canyons and mountains. All of it with the western sky thrown in for no extra charge. You can't go wrong.
Bob