Joshua Tree is a beautiful and unique National Park that is ~45 minute drive from Palm Springs.
A very fun art museum to explore or even just walk around to see the sculptures outside.
An air tram that will take you to the top of a mountain to take in the gorgeous views.
If shopping is more your speed, the Cabazon outlets is a massive outlet mall with stores for everyone ~25 minutes out of Palm Springs.
There are also plenty of beautiful hikes! Here are a few of our favorites: North Lykken Trail: https://www.alltrails.com/trail/us/california/palm-springs-museum-and-north-lykken-trail (~3 miles out and back) Araby Trail: https://www.alltrails.com/trail/us/california/araby-and-berns-trail-loop (4 mile loop- you can see Bob Hope's old house) Ladder Hike https://www.alltrails.com/trail/us/california/ladder-canyon-and-painted-canyon-trail--4 (more of a full day excursion- 1 hour drive and ~5 miles but gorgeous!!)