For active Native American communities in the southwest, your best bets are along the drive along I-40 from Flagstaff, AZ to Albequerque, NM. East of Flagstaff, you will be passing along the southern edge of the Navajo reservation.
The Navajo were traditionally nomadic and so did not have large villages or pueblos, but if you get off the highway to the north, you will see many traditional Navajo hogons (small 6-sided cabins) as well as old trading posts (the best are at Tuba City, near Page and Ganado north of Winslow). Canyon de Chelly National Monument is a great spot to visit. It is scenic canyon filled with prehistoric cliff dwelling and pueblo ruins and still populated by Navajo. You can hike to one ruin or take jeep tours to see the others. It is about 2 hours north of I-40 though.
The Hopi Reservation is located on a mesa top in the heart of the Navajo Reservation about an hour and a half north of Winslow. The Hopi (a very different culture from Navajo) live in a number of mesa-top pueblos. There is visitor center and small museum in the middle, but it is difficult to get access to most of the pueblos here.
In New Mexico, there are a number of pueblos and other Native American villages on either side of I-40. Zuni (just south of Gallup) is worth visiting. But probably, the most spectacular in the southwest is the ancient mesa-top village of Acoma (southeast of Gallup) which includes classic pueblo buildings, a large spanish mission, and virtually no modern buildings. You can only visit as part of a tour (well worth it) which run daily.
Chaco Canyon National Park (about two hours north of Gallup along rough roads) is filled with famous prehistoric ruins (some of the largest pueblo ruins in the US) and very interesting if you have the time.
Although it is not a Native American site, be sure to check out the historic La Posada Hotel in Winslow - one of the last of the great Fred Harvey Santa Fe railroad hotels - and recently restored to its original grandeour. The resturant there is really good too.
Taking a more southern route (I-10) passes by or through some Indian Reservations (Pima, Papago, Apache) but there are few cultural sites or museums and relatively few major prehistoric ruins. Casa Grande ruin (prehistoric Hohokam adobe building) south of Pheonix and Gila National Monument north of Silver City, New Mexico are probably the best.