Don't know whether desert is familiar to you or not (I live in the temperate north with 4 seasons, snow and green farms/forests, so dry desert has the appeal of the unusual to me).
The Grand Canyon is truly impressive. Highly recommended. The visitors center has neat displays. You can either walk the rim of the canyon or can even venture down (and back up) trails that take one to the bottom. There are services for hire that take you for raft or boat rides. There's an Imax theater that shows the super wide screen that gives the impression of being right on a raft where the water splashes in your face. 1.5 hour drive north Flagstaff (Flagstaff is about 2.5 hour drive north of Phoenix). I can still remember how awed I was the first time I saw it, only previously having seen black and white 2x2" photos from a grammar school book, which can't convey the immensity of the Grand Canyon.
Sedona, Arizona is a New Age spiritual mecca (one of the energy vortexes touted in the '90's Harmonic Convergence), a large village nestled in a Red Rock valley. Lots of high end tourist shops with Southwestern (American Indian) motif-type items. Picturesque 1/2 hour drive on Rt89A on the hairpin turn canyon road between Flagstaff and Sedona. There are activities like Jeep rides through the Red Rocks. Classic American tourist spot (hundreds if not thousands of timeshares in Sedona)
Jerome, Arizona is an old mining town perched on a mountainside. Lots of rickety old wooden buildings on the mainstreet. The signs outside the bars make it clear that it's a criminal offense to enter with a firearm. The flavor is cowboy-western-mining.
The I-17 interstate highway that runs north from Phoenix to Flagstaff run through areas with lots of giant cactus (Saguaro?) the icon of Arizona.
Death Valley National Park (northeast of LA) is the hottest, the lowest (elevation) and driest part of the USA. I can only wonder in amazement at those who survived crossing the barrens on foot or with a horse/ox drawn wagon.
15 years ago, the Long Beach airport (due south of LA) coffee lounge was an art deco wonder. On the 2nd story, it looked out over its airfield and the adjoining airfields and one could imagine Howard Hughes drinking coffee at the next table. A throwback to the 1930's. It was worth a couple bucks for parking and a buck for coffee just to soak in the ambience. Don't know if the coffee shop still is 30's art deco, though. Hughe's "Spruce Goose" airplane flew in the water just offshore, but I think the plane itself has been moved elsewhere.
Somewhere in LA is a museum of artifacts from antiquity, like a sabretooth tiger, that have been preserved in the tar pits of LA. Probably the tarpit museum?
Dan