Check out the Tram for an amazing view of the Coachella Valley. This is a 10 minute tram up to the top of the mountains (about 8,000 feet up) with hiking trails and a restaurant at the summit. Be sure to bring a jacket as the temperature difference is typically over 30 degrees cooler at the summit. Tickets can be purchased ahead of time.
About an hour drive from Palm Springs, you can explore Joshua Tree National Park!