Colorado River, Elsinore are the two closest public, non expensive bodies of water....both within two hours of Palm Springs.
Shadow Lake (Indio) is private and you have to own or be with owners to ride there......and it is one of the best private lake communities out there.
Sunset Ranch is best for week long or weekend stays. The house can accommodate many many people and the trip would be similar to a houseboat.....but it is rather expensive. The lakes are VERY shallow...probably only 5 feet at the deepest points....
I live in the PS area and unless I get a rare lucky pull at Shadow Lake, we usually ride the River or Elsinore. Hit me up if you feel like it 760.275.4073.