Hi Mark,
How exciting ! OK...
In Las Vegas, The Strip, or Las Vegas Bvd, is right next to McCarran airport, so if you are near a window that side, it is a good photo as you land.
The Strip is about 7 km long, and you just can't see all of it in detail in a day or 2, but a walk up and down as much as you can is worthwhile, especially at night. Alternatively there is a monorail, which runs in the back of the major casinos, terminating at one end in the MGM Grand. From there it is a moderate walk to the Excalibur, and a couple of other shorter monorails between the casinos. The Luxor is worth a look inside for its strange pyramid construction.
http://www.vegas.com/transportation/monorails.html
Do research on the free attractions, and what time they are. The Sirens show at Treasure Island, the fountains at the Bellagio, the volcano at the Mirage, and Fremont St, are all good. The best way to see the big casinos is to go into the main lobbies and look around there. Further on, they are more similar, with hundreds of poker machines in long rows.
http://govegas.about.com/od/cheaplasvegas/a/freelv.htm
http://www.vegas.com/attractions/freeattractions.html
On the way to the Grand Canyon, you may want to go down to the Hoover Dam and have a look around for an hour. The highway now goes across a huge bridge above it, but you cannot stop, and you will be on the side away from the dam, so you can still divert down the old road, Route 172, and drive across the dam. You will need a map to find the exit.
http://en.wikipedia.org/wiki/Mike_O'Callaghan_%E2%80%93_Pat_Till man_Memorial_Bridge
At the Grand Canyon, there are some restrictions on where you can drive your car. I'm referring to the South Rim. However there are free shuttle buses running around all day every 10 min. Do take the one out to Hermit's Rest, from near the Bright Angel Lodge. Along this there are several terrific look downs, and you can step off the bus, take photos, and then board the next bus.
http://www.nps.gov/grca/planyourvisit/shuttle-buses.htm
If it is raining, take your umbrella or coat, because there are not many shelters. Also visit the area in the back of Kachina Lodge, and you might see a California Condor. They sometimes land there to look at us !!
Be at the Mather Point lookout just before sunset if possible, the colours are beautiful - photo attached
Cheers