Responding to the OP you have three ways to get from the Long Beach Airport to the DLR. If you exit the airport and drive straight ahead you're on Wardlow Road, which eventually turns into Ball Road which is the road on the north end of the DLR. If you take this route, about two miles from the airport is a Ralph's on the right. Stay on Wardlow, then Ball Road and you'll end up at DLR in about 30 minutes total.
If you turn right out of the Long Beach Airport on Lakewood Blvd, you'll come to the 405 freeway, go south until you get to the 22 freeway, then get off on Harbor Blvd. On Harbor, near the freeway is an Albertson's. This will also take about 25 to 30 minutes to drive.
If you turn left out of the Long Beach Airport and go up to the 91, then the 5 toward DLR I'm not aware of any grocery stores along that route.
Near
Disneyland are some 7-11s and there's a Target (not a Super Target) on Harbor. Their selection of groceries is very poor. There's a Ralph's on the corner of Euclid and Chapman, but I've never been to that one.
We're going to VGC on Monday for our FIRST VISIT!