Palm Desert is just a short jaunt away from Palm Springs so, as mentioned, PS is a great location for attractions.
My suggestion is to walk the
Indian Canyons trails--an amazing literal oasis of palm trees and creeks in the middle of the desert. Google some pictures, it's worth it.
I remember walking those trails as a kid, back in the '50s with my parents, and I still remember the experience.
Of course, there is the tram up the mountain for a fantastic view of the entire valley.
