If you're just going to do the Strip, I'd go with the Monorail.
The closer you get to the Strip, the more idiots driving badly you'll encounter. When I worked on the Strip, I parked at the Hilton (now Westgate), which was the easiest resort on the Monorail system to reach from my house. Then I commuted to work from there. If necessary, I could make it all the way down to Mandalay Bay using the Excalibur to Mandalay mini rail.
It's not that big a deal to walk from Flamingo to Caesar's or the Bellagio, either. We also used this for going to Sterling Brunch, which pours Perrier Jouet champagne as their all-you-can-drink. We'd take a bus to the Hilton/Westgate and then monorail to Bally's/Paris. The best part is that since the average tourist isn't going to walk (heaven forbid!), unless there is a big convention you usually have the monorail to yourself.
As for the Grand Canyon, take a helicopter. Seriously. Everyone makes the same mistake -- they wake up at o-dark-thirty, drive six hours to the Canyon, spend 15 minutes looking at it. And the six hours back. I had to make that trip one too many times for family members. After six hours on the road, nobody is really up for doing anything. The new bridge over the Hoover Dam cuts a hour off the trip, and it still takes forever.
