Gareth,
I've lived in Las Vegas four times during my career, and flew tours out of there for a couple of years; primarily in the Grand Canyon.
First, I'll admit I'm biased; I hate Vegas about as much as I hate anything but dental work, and I really hate dental work. I turned down a great flying job there not long ago; not because of the job but because I hate Vegas. That said, if you must go there...have a good time.
Rentals...take your pick. Call ahead. If you're going to be flying the Grand Canyon, bear in mind it's a busy place, and the only eyes protecting your back are your own. You really ought to get hold of a Grand Canyon chart and review it very thoroughly before you go, and you really ought to have someone in the airplane who's checked out on the canyon, the procedures, and the area before you go.
A 172 does fine out there. I've spent many hundreds of hours down in the canyon and flying in and out of landing strips in the canyon in 172's and other light airplanes. Watch your performance, know your performance, and remember the water principle. Water flows downhill and so do you, and that's your escape. Weather can change rapidly in the Canyon; the Grand Wash cliffs to the west of Canyon West can force air upslope rapidly, changing a clear day to mud and sleet and ice in short order. When the Canyon does go down, you need to be able to look down at any point in it's 277 mile length that you intend to fly, and know exactly where you are. If you can't do that, then get someone to go with you who can. Just up from Diamond Creek, opposite the Parashant Wash, is the outline of a Navajo etched in the cliff, including the circular prop marks, at a spot called Gus's Plateau. Gus was the pilot, and thought he was turning up Canyon and making a run to head for South Rim. He picked the wrong canyon, and his remains and those of his passengers will be forever in the rock and down below. Don't join Gus...or many others who have been in there when they shouldn't.
Remember that flight in the canyon areas can be very turbulent; take plenty of sick sacks for your passengers. It's not a jaunt over Coventry. You have fewer options for airfields, too, no radar coverage, limited communications, and if you lose an engine, your planning moment by moment will be put to the test.
It's a beautiful area to fly. There are a LOT of retrictions out there now with the airspace as it is; be aware of them.
Don't overlook Henderson or Boulder City as places to go; they're a lot less busy than North Las Vegas, not at all far away. You might consider driving up to St. George and renting there. It's a couple of hours away in Southern Utah, but there's plenty of scenery there too, and you can easily fly to Bryce Canyon, Zion Canyon, the Grand Canyon, and Lake Powell. There are several places there to rent. I don't have the info off the top of my head, but you can find it online, I'm sure. Cedar City just north of there, too.