Canyon De Chelly is a beautiful place. I did the shake and bake tour a few years back, and wish I had driven. There is no difficult wheeling that I saw - just some water crossings and sand, as I remember. John is right about the requirement to hire a guide to drive it - from the desertusa.com web site: "To drive on the canyon bottom, a 4-wheel drive vehicle, a Park Service permit and an authorized Navajo guide are required. The fee is $15.00 an hour for 1 vehicle, $5 an hour for each additional vehicle with a 5-vehicle limit per guide." And of course, the obilgatory gratuity. The whole place is on the Navajo reservation, it is at a decent elevation (5000 - 600 ft) and the place is rolling plains/hills with a suprise canyon you don't expect until you come upon it. The canyon is like an oaisis in the high desert. It gets hot in the summer and cold in the winter - I went labor day and it wasn't to bad, but we got a little roasted in the lorrie. Spring or fall would probably be the best times to go.
Carl