It's a great thing to do, but you need to be really sure what you're doing. There's a special paper chart for it showing all the various corridors. It hasn't been updated for a long time but it is still the valid one.
iirc, below 18000 feet you are only permitted to fly certain corridors, and even so only quite high, to keep you out of the way of the tourist flights. They operate under special permits, which you will not be able to get. You can't get even close to the canyon rim, and you certainly can't fly below it.
I did it once but unfortunately there were forest fires and the view wasn't that great.