Palm Springs has lots to offer for all interests, and is surrounded by mountains, the Joshua tree national monument also lies to the North.
Hiking enthusiasts can hike the Indian Canyons, a natural oasis full of palm trees, accessed from just down Palm Canyon Drive. This area offers a variety of day hikes ranging from stroll to strenous. The Terrain includes stream beds, palm groves and cactus filled mountain sides. Other canyons around Palm Springs offer more trails. Here is a great web site with hiking information for the area http://www.hiking-in-ps.com/
Joshua Tree National Monument is a large National Park where two types of desert come together, the Colorado desert, and the higher Mojave. Rich with animals, wildflowers, strange geology, and of course the eerie looking Joshua trees Joshua Tree Park
Taquitz Canyon has hiking trails leading to the falls and back on a two mile loop, with pools an desert flora.
San Jacinto State park includes the 2nd highest mountain range in California, and also has a wide range of trails.