Please let us know the number of people and their favorite activities (theatre, pro sports fans, hiking, windsurfing, biking, restaurants, shopping, etc.)--and the amount of time you have and I'll give you more specifics.
As a beginning:
Theatre--Utah Shakespeare Festival (relatively inaccessible, over in Cedar City, Utah)
The Guthrie Theatre in Phoenix
Scottsdale Center for the Performing Arts
Warning: real temperatures in Phoenix often hit the mid 110's. No typo.
Pro Sports: Arizona Diamondbacks
Hiking: Lots of good trails in Prescott, Sedona, and Flagstaff. Or the Grand Canyon. If you want to climb, you can try hiking from a base of about 8800 feet up to over 12,000 feet on Mount Humphries, outside of Flagstaff.
Sedona has some beautiful scenery (beautiful red colored rocks) if you're not burned out after the Grand Canyon.
Another post mentioned Meteor Crater. It is out of the way but a fascinating trip.
For a side trip, try Tombstone (yes, Wyatt Earp and all that).
Halfway between Phoenix and Flagstaff, you can try Montezuma's Castle -- a series of caves inhabited by Anasazi Indians, IIRC. Or you can drive up into the mining ghost town of Jerome (lots of fun mountain curves on the way there; when you get there it is a contest between Harley Davidson riders and the arts-and-croissant crowd as to who is re-populating the town...)
Windsurfing--Lake Roosevelt, Lake Pleasant, or Tempe Town Lake.
Phoenix has numerous water parks, or you can ride an inflatable inner tube for several hours on the Salt River.
Biking--Mountain Biking in Sedona is great; there is also a trail going 70 miles from Flagstaff to the Grand Canyon.
Another poster mentioned some great mountain biking in Utah.
Restaurants: Scotsdale. "What does a Scottsdale housewife make for dinner?" "Reservations." Enough said.
Or try Tempe (home of Arizona State University)-- the town there has a lot of restaurants in a small area.
Shopping -- tons of high-end shopping in Scottsdale, plus Arizona Mills, Anthem has an Outlet Mall, Paradise Valley Mall...
As for California:
Northern or Southern?
If Northern, San Fran is quite the place to visit, but be sure to take a detour through the Sequoia forests, there is one park where the road is carved through a Sequoia.
And of course all the nearby wine country in Marin County.
San Diego:
Beautiful, cool, ocean. What more could you want?
There's Sea World.
You can take a tour of the retired aircraft carrier Midway (I got to go camping on board with the Boy Scouts once).
LaJolla is full of shopping and restaurants I'm told.
Santa Barbara is beautiful.
Stay away from L.A.
Oh, yes, you could try (out of one's way) go to Four Corners--where Colorado, Utah, Arizona, and New Mexico meet. There is a little benchmark / plaque there and you can literally stand in four states at once.
Hope this helps, be sure to ask if you have any questions.
Cheers!
There will be 3 including a 15 yr. old boy. Trip time will be 16 days. And we are driving. Its meant to be an educational trip. Museums, famous homes, national parks, etc.