I would look at staying at Oahu the whole week. If you've never been before, there's lots to do for a week there, no need to Island hop. Island hopping is going to add to your airfare prices. And I would pick Oahu, because there's lots for teenagers, and it's the easiset island to navigate without a car. Rental car, gas, and hotel parking will easily run you $1000 on a 1 wek trip. The buses very easily take you from the Waikiki area, to most of the other areas. And also look at riding the buses vs. a tour group. The tours are expensive, and you can do the same thing, for way cheaper, just using the busses. You can take a bus to diamond head and hike for free. Take the bus to pearl harbor and do the tour ourself. The USS Arizona Memorial is free and the bus is like $3/person each way, but the tours charge $30-$50/person. Take the bus to haunama bay (I know that's spelled wrong, but someone should be able to correct it) and snorkle. Again, the tours go here for much, much more. Take the bus to the Ihilani Palace and do the self guided tour. The self guided tour shows the same exact things and discusses the same things as the guided tour, just allowing you to go at your own pace and save money. Take the bus to Ala Moana Mall and shop. Take the free shuttle to Hilo Hattie and shop. Aside from that, sitting on the beach is free and that's the best part of Hawaii anyways

Also, on waikiki beach, they have stands where you can rent a surf board, water bikes, kayaks, etc by the hour or day, and they are really reasonable. I think we paid about $10-$12 for 2 hours on those water bike things the last time we were there a year ago.
Also pick up the little red coupon books on all the corners. They have discount coupons for helicopter rides over the Big Island volcanoes, the catamarran boats, surf lessons, restaurants, etc.
Many people are going to say oh the food is so expensive, but we don't find that to be the case. The prices are a little higher than at home, but not significantly. They still have chain restaurants: California Pizza Kitchen, PF Changs, Red Lobster, Outback, Bucca Di Beppo, etc that are all priced maybe a couple dollars higher than at home (Just mentioning incase your kids aren't adventerous eaters) They also have some really nice, expensive restaurants and eating there would add up and be expensive, but so would eating at an expensive restaurant every night at home... If you're really trying to eat cheap, there are a lot of sushi/noodle bowl/teryaki bowl places. They serve giant bowls of japenese ramen like noodle soups with chicken or beef, teryaki rice bowls or lunch boxes and limited sushi offerings and they're all really, really reasonable. We like the noodle bowl place in Hilton Hawaiian Village and the bowls were around $6 each. Across from Hilton Hawaiian Village is Wailana Coffee house. They have an all you can eat pancake breakfast for $4.99/person. So there are plenty of affordable places to eat, if you look.
Good luck planning, and if you have any other questions or need help, just ask!!!