We almost always stop on the way to the resort (we stay at the Marriott Ko Olina right next to Aulani) and get enough at Target to hold us over the first night. Then the next day, we go to Costco (and usually back to Target) for a bigger grocery run. But, we keep a car the whole time we're there. I wouldn't ever not have a car there!
Once we get to the resort, if the room isn't ready, they can keep your things that are cold or frozen in a fridge or freezer for you.
We're just too tired after that long flight (we come from Maryland) to go back out, so like to do this if possible. Once we did go check in, and while my DH was swimming with the kids, I went back to Target to buy our stuff. I was beyond tired! But that year we didn't even bring toiletries (just brought carry on bags) so I needed to get shampoo, toothpaste, etc... plus bottled water, breakfast foods, lunch foods, beer, booze, wine, juice, milk, etc... Nice thing is the bell services have huge bins to fit all the grocery bags in, so it was easy for them to haul it all up to the villa.
This next trip I need to remember, Target does NOT have free bags. Bring reusable shopping bags! The new law went into effect last year that banned plastic bags of a certain thickness on Oahu.