The ghost town of Amboy, the Mojave Reserve, Death Valley, are all in a day's drive. East of Palm Springs at Churiaco Summit is a private museum dedicated to Gerneral Patton.
Go to the Morongo Casino and see the concrete dinosaurs. Don't forget Hadley Orchards dried fruit shop--it's incredible.
Hike to the top of Mt. San Jacinto (10,600+ feet) and visit the stone hut near the summit. Climb Mt. San Gorgonio (11,502 feet). Both mountains are right on top of Palm Springs.
Go to Mt. Palomar, and the lovely semi-ghost town of Julian.
Eat at The Hat. Eat at In-N-Out. If you drive to Orange County, eat at the Crab Cooker in Newport Beach or La Palma Chicken Pies in Anaheim.
Visit Bass Pro Sporting Goods in Cucamonga. Eat incredible ribs ar the Red Hill Barbeque there. If you have money, the Sycamore Inn there has incredible prime rib.
Go see the Planes of Fame Air Museum at Chino.
Go to Mt. Baldy and ride the ski lift.
Drive the Angeles Crest Highway.
Drive up and see the Eastern Sierra and/or Las Vegas.
See the Colorado River.
See, and more importantly SMELL, the Salton Sea. The stench is mystical.