Palm Springs (and most of the surrounding area) is pretty bike friendly and bike lanes are on most streets. I know that a couple of shops offer bike rentals, but make sure that you get a reservation as this is the start of the busy time of year for them out there.
Mountain biking out there is strange, the terrain is very desolate and there are tons of thorns. Take extra tubes/patch kit and make sure that the shop knows you are planning on hitting the trails so that they put good tires and possibly a tire liner on for you... Good trails include the Goat Trails which are on the south side of town. very technical and strenuous... but I have heard they are well worth it. Check with the local shops for route maps.
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