Joshua Tree National Park is a must see if you have some extra time. It's ~40 minute drive from Palm Springs and has great hikes, Pioneer Town, art exhibits, etc.
If you have half a day available, the Tramway is a cool (touristy) thing to do. Buy tickets at the bottom and then ride the tram up the side of the mountain for epic views. There's hikes and a lodge at the top.
Great for kids and adults, the botanical garden and zoo is a ~35 minute drive from the hotel.
The site of the wedding (Jay's parents' house) sits among many historically famous mid-century modern homes. Stroll through the neighborhood and have a look!