Janet,
One of my favorite areas for backpacking and less than an hour drive is around Mt San Jacinto. I’ve backpacked in this area many times. You can start in Idyllwild or take the Palm Springs Tram up to the top. Here’s my report from my backpacking trip up there in August 2014.
You can also backpack in the San Mateo Wilderness south of Ortega Highway, starting at the parking area across the street from the Candy Store.
And there’s good backpacking in the San Bernardino Mountains. Our last trip up San Gorgonio was an overnight backpack from Vivian Creek to High Creek, where we camped for the night before continuing on to the summit.
That should give you a few ideas to get you started. Let me know if you have more specific questions about any of these areas.
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