The closest thing to a grocery store anywhere near the park is a 7-11 on corner of Harbor and Katella. We just got back last week and when we asked the front desk at our hotel for the closest grocery store. We were told to go right (towards conference center) on Katella and follow it down for about 2 miles the store is on the left. It's a Food 4 Less. Could walk in about 20-30 minutes, but there is also bus service for a decent price. Also depending on where you're staying they might have a shuttle service that can take you there.