I stand in awe of SN3's fantastic post, but I have flown across the canyon in the VFR corridors occasionally and would like to add the following:
For a place to visit in the Canyon, nothing beats the
Marble Canyon airstrip. It's narrow, undulating and quite long (it needs to be!). There's a fairly basic motel across the street, a store and a pleasant walk to the famous girder bridges near where Powell entered the river on that first journey. There's also a private strip at Cliff Dwellers Lodge which I've not visited.
Back in 1991 the FAA published a 'VFR Pilots briefing pamphlet' describing the special rules area that surrounds the canyon and details of the corridors and 'no fly zones'. This pamphlet contains photos of the corridor waypoints as seen from the other side and I've found it extremely helpful in confirming visual / gps navigation. I have no idea if it's still available but I could scan my copy if you are interested.
I can only echo SN3's words about flying early. My own policy is to depart at dawn (US airfields open early) and get flying for the day done by 11:00 am latest. Anyway, this tactic keeps you closest to UK time and minimises jetlag on the way home!
Page is a lovely spot and will be instantly recognisable to anyone who's seen the movie 'Evolution'. I suggest staying in the Best Western overlooking the river. When you land at Page you are likely to be accosted by not one, but two FBO's. I was there in January and used Classic Aviation who were extremely helpful.