Indeed. If you are in Indio, go to Joshua Tree National Park. I always take the 4 wheel drive trip up through Berdoo Canyon, it quite the adventure. Since this is the "back door" entry you won't pay park fees. Just make sure you return through Berdoo Canyon or take Cottonwood Springs road back to Interstate 10.
You could also try a day trip up to Mecca Canyon and hike Ladder Canyon. It's very nice this time of year.