I haven't geocached in any of the areas you're visiting, with the exception of the Grand Canyon. Since it is a national park, the only caches there are virtual. And because of the location, ALL of them are GREAT!
I don't know if you will be visiting visit Flagstaff (about 30 or 40 miles east of Williams on I-40 and MUCH nicer!), but a couple of my favorites there are "Galaxies Among the Pines [a night cache]" (GCPAJP ), for a nice, cool evening walk along a nice trail among the pine forests in the area, and "Wednesday" (GCM9AC), for the great view of the San Francisco Peaks from the high meadow where it's located. Another good one was "25 on 66" (GCE7D7 ), a two stage multi that requires use of the UTM format for coordinates in your GPS unit. -- ORR
"Wildness is a necessity." -- John Muir
"When you go to hide a geocache, think of the reason you are bringing people to that spot. If the only reason is for the geocache, then find a better spot." – briansnat