If you stay 3 weeks you can do an interesting round trip.
Pacific coast north then inland over Crater Lake to Mt. St. Hellens.
Then over Salt Lake City south to Brice (nice stayover for a night in the park)
Get a Map of the Grand Canyon since there are some flying zones you can crisscross there. Preprogrammed handheld GPS is a good help. Page is a good stop. Then go to Canyonlands along the Colorado. Fly to the Monument Valley You can barnstrom there at 500 feet between the mesas. Flagstaff (perfect FBO and nice town to spent a day or two) Then go south to Tucson, Davis Montan airbase and Pima air museum worth a visit with two nights there. With a 172 and two persons and 3 weeks to spent no problem at all. You will get hot and high operations at Bryce, Flagstaff, Lake Tahoe.
See that you get an 180HP bird.