California desert -- lodging and eating recs please

We are planning a trip East from LA between Christmas and New Years, wanting to spend some time exploring the California desert. By this we DON'T mean the Big towns like Palm Springs as much as the "real desert." It will be a first time for us, so all your recommendations are welcome. Our ultimate destination will be more determined by the other amenities (lodging, dining, what to do).
We'd like to be able to hang out at a place where we can really relax (though not too expensive please) place and do day or half-day trips from there. Chains are not our style! As well, we like to explore new/interesting places to eat and while we don't expect haute cuisine there, an area with some fun (and good!) eating places nearby to check out would be a definite selling point! Hot tubs or hot springs, interesting places to hike/walk to, desert wildlife and plant life, antiquing and junking are also of interest.
Many thanks in advance for your suggestions.........................