There are tour operators who make flights from LAS to the Grand Canyon and back daily. Probably the easiest thing to do. There are special air space rules for flying over the canyon.
If you don't have a FAA certificate, you won't be able to rent a plane in the US.
You could go up for a lesson without a whole lot of instruction going on or a sightseeing flight but the sightseeing has to be within 25 miles of the airport you start at as I recall. The canyon is much farther than that from Vegas.