Search for other threads about Aulani and you'll find more advice. As someone who has lived here since 2002, I suggest you spend time on the Internet looking up info about the island and fun stuff to do and make the effort to see Oahu- it would be a shame to come so far and only see the Ko'olina development, which is where Aulani is located. Check the maps and you'll see it is on the West side of the island, and the development has 3 other resorts, a golf course, and an area with a few restaurants and shops- all higher end.
Kapolei and Ewa (say: Eh-vah) are nearby, just down H1, and have regular stores like Target, Walmart, and Kmart, chain eateries, groceries, a new mall, and a Costco. If you have a car and venture out, you might enjoy shopping there and can pick up Hawaii trinkets much cheaper. I know that Walmart and Kmart both have a section catering to tourists with the usual gift stuff. Waikele Outlets are about 15 minutes on H1, and have more of the usual outlet stores and a few eating spots.
I would suggest you do not go further up the West coast with the intent to shop- there are good people there, but it is not an area for tourists to be hanging out. It can be a rough area and even my local friends do no frequent the west coast area past Ko'olina. There are stunning beach views on the west coast, however, particularly near the end of the road, but again- it is not an area to hang out.
Your kids might enjoy Kualoa Ranch, Polynesian Cultural Center (fantastic place!) and it's show, the Pearl Harbor area ( the memorial, USS Missouri, Pacific Air museum, and Bowfin sub), Punchbowl Cemetary, Aloha Stadium swap meet (Google for times- is good for trinkets and local flavor), and Haunama Bay for snorkeling (go early! It fills up very fast). Downtown is crowded, busy, and touristy, but you might consider Bishop Museum for local history and Ft DeRussy (downtown on the beach with a military museum). Another fun activity is a train ride on the Hawaiian Railway Society. It's about 15 minutes from Aulani and you actually cross the tracks getting to the resort. It is a beautiful ride along parts of the west coast and the only train on the island.
If you like beaches, there's tons but always check the conditions and heed all warnings- some are too rough for all but the strongest and most experienced swimmers. There are also many hiking trails, but you need to read up on them. Be careful if there are clouds at the top of the mt where you are hiking or if rain is predicted. Streams fill up fast and people drown or get stuck all too frequently. Diamond Head or Koko Head are both good hikes with great views, as is the short hike out to Makapu'u Lighthouse.
If you live with horrible traffic, you'll feel right at home here between the hours of 4:30-8:30am and about 4p-7:30p when H1 is packed and traffic crawls slowly. It is not uncommon for traffic to simply stop, and an accident will tie up traffic for hours. Most areas of the island (North shore, West coast, east areas, etc) only have 1 road, usually 2 lanes, so traffic can easily back up for no particular reason except it is a busy time.
Do NOT leave valuables in your car, especially within sight. Theft of items from cars is common here, especially in tourist areas. Locals are very friendly, talkative, and can give you good pointers. Aulani is a beautiful resort with an amazing pool area that your kids will love. Have fun!
Edited to correct a date- been here 14 years, not 4!