I did the Route 66 tour 2 years ago and the itinerary has changed a bit, we stopped in Kingman instead of Las Vegas and never went into Vegas. On our tour we left Flagstaff and travelled up to Cameron (about 50 miles) and stopped at a Navajo? Souvenir Shop and Cafe this is at an area called the little grand canyon as I remember. From there we went in to the grand canyon park and stopped at various points along the southern rim, the watchtower and at grand canyon village for lunch. We then travelled on to Kingman stopping off at Seligman on the way, Kingman looks to be about a hours drive from Vegas.
Having been to Vegas a few times I guess the trips to the canyon will be to the western rim with the skywalk. You can fly there from Boulder City airport about half a hour away from Vegas and the flight on a small prop plane takes about half a hour. Also done it on a coach and the drive takes about 4 hours with about 10 miles of it off road. The plane lands on an airstrip at the side of the canyon and the local native indians Hualapi? have set up some facilities there a wild west town, indian settlement, the skywalk, and the wreck of an old bird guano mining facility. The canyon itself in this area is not as scenic as the southern rim in my opinion but eagle point is good.
Hope this helps.
Regards,
Steve
