You can find a Trader Joes in one of the towns in that area, stopped on the way from the NHC to stock up on food for the stay in the Desert.
If you are going to/from Joshua Tree NP, take a detour and go up to Pionertown. This is a town built for the sets for TV and movies after WWII. Think Cisco Kid for example. There is a roadhouse named "Pappy and Harriets". They have at least Sierra Nevada Pale Ale on tap, good BBQ and grilled food, and a killer Texas swing band playing the first night we stopped in. Liked it so much we went back the next night. It also was on the last "No Reservations" that we watched, so it might become too popular.
EDIT - There is a Trader Joes in Palm Desert.
Go to the Trader Joes and do the store finder for Palm Desert. OK beer selection, might be good for that area.