It is best to plan out getting groceries and supplies down the hill before you get to Green Valley Lake. There is no close full size grocery store in Green Valley Lake.
At the bottom of the hill the last city you go through before the 330 is Highland. In Highland there is a Super Walmart with supplies & groceries, Albertsons, Stater Bros, Food for Less etc.
If you need a grocery store after you are on the hill, here are your options.
6-7 miles away in Running Springs and a 15 minute drive in good weather & traffic
Small grocery store with most standard items, more expensive than other stores, very small meat & produce section
31987 Hilltop Blvd, Running Springs CA 92382 (909) 867-2228
15 miles away in Lake Arrowhead which is about a 25-30 minute drive in good weather & traffic
Full size grocery store, same prices as down the hill
28100 Hwy 189. Lake Arrowhead, CA 92352 (909) 337-5854
22 miles away in Big Bear which is about a 40 minute drive in good weather & traffic
Full size grocery store
42170 Big Bear Blvd Big Bear Lake, CA 92315 (909) 866-6027