Gallup is........... interesting, easily the most cosmopolitan place in New Mexico, with Navajo Indians, Zuni Pueblo Indians, Hispanics, East Indians, West Bank Palestinians and some very eccentric anglos thrown in the mix. Not the least bit pretty, though, although the countryside around there certainly is.
If I wanted to do the rez, by train, I would stop in Albuquerque, and take the new Railrunner to Santa Fe, about an hour and a half and $8. No service on Sundays. Very good connections to the tourist areas from the train. It passes through three or four pueblos along the way. Like trains everywhere, it passes through the back side of the Pueblos and you see stuff you would never see from the road. I like the abandoned curio shop on the left side of the train as you approach Santa Fe, painted in garish but faded colors with a sign saying "See Live Indians!" and "As seen in Life Magazine!"
The best place to buy a good rug would be the Santa Fe Indian Market, which is August 19 this year, I believe. Go to one of the larger auctions. Prices have been soft on Navajo rugs for some time, and this year ought to be a barn burner. Its a dying art, and this is the time to build a collection if you are so inclined. Next best choice would be Gallup.
I think I would rent a car from Albuquerque after I were done with Indian market. (Indian Market is the biggest deal of the year in Santa Fe, so its probably worthwhile to stay in Duke City and take the train up in the morning).
From Albuquerque, head west on I-40. Check out Acoma Pueblo along the way. turn off the road in Grants, 40 miles west of Albuquerque, and take the parallel two lane road that runs from the South of Grants and goes through Ramah Navajo and goes to Zuni. Check out the fetishes there. Be sure you stop at Inscription Rock, the second oldest National Monument. Then 25 miles north of Zuni to Gallup for the evening. All that is a reasonably leisurely one day trip from Albuquerque.
Stay at a good cheap hotel in Gallup check out the Indian traders (don't expect too much, everything is kind of cleaned out for Indian Market) and then 25 miles north to Window Rock. Take the road from Window Rock (now paralleling I-40 but from the North) to Tuba City, then down to Flag for the end of your trip, or north to the Grand Canyon. Stop at the Hubbell Trading post in Ganado, Canyon De Chelly, and a Hopi village or two. Plan on spending the night at Canyon de Chelly. The Gallup Indian Ceremonial is also a huge deal, usually a week or two before Santa Fe Indian Market. Well worth it. Or, you could do the Navajo Nation Fair, usually a week after Labor Day. the Navajo Nation fair is 100% authentic Native American, that's for sure. Its not the least bit threatening, but you will be outnumbered about 100 to 1 by Navajos.
Get on I-40 and burn up the road to Albuquerque from Flag. Maybe 5 hours or so on the interstate.
Sorry for the long-winded travelogue.