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If you really want to see the Grand Canyon, another sight or two, and drive old Route 66, then this simply can't be a day trip from Las Vegas. You'll have to spend a night (at a minimum) somewhere on the road. I'd almost say that for sure, even if you just were just going to the Canyon. Also, the only way to do what you want is to go to the South Rim, which is actually where the vast majority of the images of the Canyon you've seen were shot. The South Rim also has the advantage that there is a road along a roughly 25 mile section of the Canyon, whereas the road into the North Rim goes only to a single location.

The longest remaining section of old US-66 is now marked as AZ-66 between Kingman and Seligman going through Peach Springs. Note that once you start down this road you are pretty much committed to going all the way, there are no easy ways back to I-40. Other attractions that you should consider, depending on your tastes, are the Navajo Trading Post at Cameron, Wupatki, Sunset Crater, and Walnut Canyon National Monuments, and Lowell Observatory and the Museum of Northern Arizona (anthropology) in Flagstaff.

AZBuck