Hi! We own at the Marriott's Ko Olina (nextdoor) and live in the DC/Baltimore area. We go every other year (and also used to live on Oahu for 3 years).
I started taking my kids back when they were 4 and 6, and have been several times now. I've gotten really good at pooling and hoarding our frequent flyer miles, so we've always gotten free tickets (yes, always!). The key with that is to start looking 330 days out and wait until a good redemption is available, and it's harder to get 4 tickets at a time. Realistically, it's probably closer to $800 or more for a coach ticket from the East Coast, but it depends on the time of travel. The $300 to $400 ones are usually from the West Coast.
We always go with one stop, either Atlanta, Chicago, DFW. If you're looking for first class (we went last time and will again this year) Delta (via Atlanta) and American (via Chicago or DFW) have the almost lie flat seats. I got Delta in 2009 and again for this year - and it's so nice to lie back and sleep. Cost this time was 85,000 miles per person.
I definitely recommend looking into only one plane change - it's a long enough trip as it stands!
I'd go for at least 10 days. We have previously gone for 11 each time, but this year we're going for two solid weeks. It's nice to get settled into the condo and relax...
Right near Ko Olina is a brand new Super Target, a wonderful Costco, as well as Safeway, so within a 10 minute drive you can really stock up on great meal ideas. We get fresh fish, sashimi, fruits, salads, and wines at Costco, and fill in at Super Target and Safeway. We end up cooking probably 2 meals a day in our condo - they have gas grills at the Marriott, and they're always so busy every night! It's a fun way to meet other guests, and an easy way to make a great dinner (we usually do fish but sometimes other things like burgers).
Our day is usually a morning snorkel, then rest during the noontime and have lunch, then back out to the pool, then grill dinner. I usually spend a lot on groceries, but we eat so well and spend less on restaurants.
You will definitely need rental cars.