I can't comment on shipping boxes; I'd call the resort directly.
We actually own at the Marriott next door, and have lived on Oahu (1995 to 1998). Been back about 10 times so far, and love the Kapolei area.
Suggestions for restaurants: if you like sushi (and don't mind waiting outside for about an hour - or try off times but still a wait) Sushi Bay is amazing! It's right by Safeway in Kapolei (10 minutes away). They also do take out.
Other than that, we eat out little in this area. We do love Willow Tree in Kailua (if you take a drive up around the windward side).
Do NOT whatever you do, buy pretty much ANYTHING at the Dole plantation. Seriously. They had chocolate covered macadamia nuts for like $67 for a pack of 6 boxes. Costco has a 12 pack for like $30.
Costco is your friend. Pick up whatever you can't get there at
Walmart or Target. All 10 minutes away. And, they all sell wine, beer, and liquor.
We've gone for 2 weeks before with just carry on luggage. We just pack clothes and one extra sandal pair. When we're checked in, I go to Target and pick up our initial supply of water, breakfast foods, soy milk, WINE, and toiletries. Of course I'm exhausted but it's all good! Next day we do a Costco run. Do laundry every day - don't need much AT ALL in Hawaii really!
Hope this helps!