We were in Vegas for a week in February about five years ago and we rented a car, which is what I'd recommend. We drove to the National Park/south side, stayed the night near the park in Tusayan, and went back the next day.
It's a five-hour drive one-way from Vegas, and although driving through the desert is boring you can stop at the Hoover Dam for a couple of hours and some other places along the way.
Kingman is interesting because there's a massive airfield on the north side of the interstate where they store planes that are going to be decommissioned. At that time about a quarter of it was DHL airplanes. We actually saw a smaller Delta commuter plane being chopped up with some pretty fascinating equipment. I got out and wandered near a hangar and there's a sleepy museum in there that's manned by some retired veterans. They have all the time in the world to talk. I was nice and made a donation and he surprisingly let me into the airfield to look at all the abandoned planes. If you try to find this on Google Maps you can't as everything has been scrubbed so you can't see any of this (unless it's actually been completely obliterated since then).
The national park is incredible and I'd think you want to take as much time as you want being there which is why I say drive, plus I just want the freedom to do what I want as opposed to stuck on a tour. When we got there the first day it was before sunset, and with all the snow (at least two feet deep) the photos were incredible. The canyon is at an altitude of about 7,000 feet so it's 7-10 degrees Celsius cooler there than Vegas year-round. Entrance to the park is also dirt cheap. There's a really good visitor center outside the park in Tusayan run by National Geographic (I think) and they had an awesome IMAX movie.
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