Choosing to stay in Flagstaff for two nights allows you to select some of the most beautiful scenery in the world. I would choose to stay home rather than rush this particular trip. You can usually only stay in the actual national park with reservations (that most Las Vegas tourists are unlikely to have arranged).
A journey could begin from Las Vegas in the early morning with an inexpensive casino breakfast. Driving across the Hoover Dam puts you on US 93 into Arizona. The 82 miles to Kingman, AZ is an interesting stretch. Look for the wooden crosses that mark traffic fatalities on the mostly 2 lane road.
Looking east, you can see portions of the abandoned railroad bed for a bit, & there are a couple historical markers worth the 60 second delay to read them. Do stop for gas and needs in Kingman. It's the best service stop on the way to the south rim. I like to carry an ice chest with cool beverages. In Kingman, pick up I-40 to Williams where AZ 64 will lead you to the canyon. The sceneryalong I-40, though not breathtaking, remains interesting.
Once there, an admission fee gets you into the park where there are many scenic overlooks. There are Golden Eagle and Golden Age discounts available. Much of the overlook views are available for the disabled, though climbing on the rocks is unwise - perhaps for all. Only rails protect you from the drop. Photography, though overwhelming, will not do justice to what's there. Air rides are available outside the park, donkey rides to the floor are available within. Reservations are usually required for the donkeys and half-day as well as full-day trips are available for those UNDER 200 pounds. You can luck out and get a cancellation to ride without a reservation. Many get scared descending the ridges. The guides will tell you to close your eyes. After all, that's what the donkeys do! By the way, I failed to qualify for the under 200, but I'm working on it! Flagstaff is about an hour away and represents the best shot at getting a room reservation, (though there are good motels in Williams, as well) except that even this may be hard during the ski season. We were at the Little America at Flagstaff in March, 1989. We were provided with free firewood for a chalet type suite. Nice place, but less expensive places are available. We were awakened to 10 inches of Easter Sunday snow! Folks were walking around in shorts before we descended to the desert. An hour later, the rental car had 6 inches of snow quickly melting from the hood into the desert. Fill up before leaving Grand Canyon, Flagstaff or Williams. On a later trip, we stayed at a Holiday Inn Express in Williams. Good basic and inexpensive. Williams is a Route 66 town with gas, a few motels and eateries. There's a good diner/bar in town, but I can't remember the name. Ask the cops since they always seemed to be there and try the pies! In this area, you can day trip to the Painted Desert and Petrified Forest. A meteor crater is near Winslow. It is interesting, but under private control and I found the admission charge excessive. On two flights, I have seen it better for free! There is also a steam railroad from Williams to the South Rim. This option will require more advance planning. But the best day trip from Flagstaff is Sedona - about an hour south. Here are the famous red mesa and butte formations that have been used in so many movies and commercials. I have found that you can photo the same formation from several angles and get totally different perspectives of the same item. There are Jeep tours available, saloons & shops galore, but pleasantly presented to not be too distasteful. While I was there, a C of C type was bad-mouthing a merchant for actually having merchandise on the sidewalk! Who ever heard of such a thing? Sedona is a plus! I heard there is a new-age group at odds politically with the old regime in this town - religion and all. Other than the mention, I will not elaborate here.
Flagstaff has the Lowell Observatory from which Pluto was discovered and the Museum of Northern Arizona with Indian culture, books and artifacts. A good meal can be had at "Cottage Place". Moderate prices, creative cuisine and impeccable service (at least in 1989). The restaurant is in an old home that was once occupied by the mayor of Flagstaff. There are a couple tables on the front porch that were especially cozy, but then, we never got to see the inside.
The drive back to Las Vegas is not too long, but again, watch your gas level and avoid the Hoover Dam crowd, if possible. Consider a visit to Laughlin!
There are many air & helicopter tours available to both the south and west rims of Grand Canyon. The free, local publications have ads and often coupons. The north rim is generally closed from October to May. It too is 300 miles from Las Vegas. Many prefer the vistas and smaller crowds on that side.