We're staying at Aulani in August and I have the same concern for my teens.
However, we were on Oahu 2 years ago, and some of their favorite things didn't cost much money.
1. Hanauma (sp?) Bay has world famous snorkeling and an incredible beach. Picture a sandy beach enclosed on 3 sides by cliffs and the ocean on the 4th. About $7.50/each to get in, $1 parking, and a few dollars to rent the snorkel equipment if you don't have it.
2. Manoa Falls - Rainforest hike with some "ruggedness" to keep it interesting. Very pretty with a waterfall at the end. Free to park in the nearby neighborhood and walk, or $5 at the trail entrance.
3. Diamond Head - The "must do" hike that's famous. Only about $5 to park, but my family also bought the tshirts with the statistics on it about the hike.
4. Tantulus Road/Round Top Drive - Don't tell your kids you're just going for a car ride as they wont want to go. However, once you get there, everyone will be impressed. It's a windy road to the top of the mountain with a few lookouts along the way. Amazing views and scenery. Free, except the price of your gas.
5. Koko Head. I loved it, the kids loved it, my wife not so much. It's a walk up a crater that utilizes an old railroad track type tram up the side. 1078 steps, almost straight up at points. Free parking at the park, short walk to the crater.
6. Pali Lookup hike. Most people park at Pali Lookout and take in the sights. If you go down to the lower level, you can walk/hike along the old Pali highway that crossed the mountain. Take this trail as long as safety dictates, there are numerous falling rock warning signs. I think $3 to park.
7. The highway around the island along the ocean is fun, again just the cost of your gas. Along this road you'll see small towns, many beaches including the famous Bonzai Pipeline, and some true Hawaiian culture such as roadside shrimp trucks. Make sure you include the H3 in your travels, one of the most amazing feats of engineering anywhere. Lots to read up on regarding the history of the H3.
8. Waikiki Beach - Some people hate it, we love it. Constant hustle and bustle, along with the ability to walk over a mile of beach from end to end. Careful you don't step on anyway, some areas are shoulder to shoulder with people which is part of the fun. Once the sun starts to set, the area immediately off the beach comes alive with people, street performers, and my kids love to visit International Village right off the beach in the evening.
9. Google Hawaii Hikes. You will find countless trails that vary from waterfall hikes to walking the ridge of the mountains. Also have your kids Google "Haiku Stairs". Fascinating history of a currently illegal hike that my kids researched only to have dad tell them "no, we aren't going to be there at 4:00am to beat the guard". Regardless, it was fun for my kids to research the hikes that are anything from a walk through the rainforest, to a walk on the ridge of the mountain with 1,000 foot dropoffs on each side.
10. Punchbowl cemetary. Caught completely off guard by this one. What teenager wants to visit a historical cemetery? However, my kids still talk about the time visiting here. Moving memorial with great view of the city. Definately not enough here for even half a day, but combined with something else it's a nice diversion. I think this put the sacrifice of lives as part of WWII in better perspective for our kids than Pearl Harbor did. Lots to read and soak in regarding the war and the lives involved.
The items above are all free or cheap. We also enjoyed Kulouau Ranch, Polynesian Cultural Center and surf lessons with Hawaiian Fire surf school, but all of these cost money. For our family, hopping to an island was over $1,000 for the day, so we didn't do that.
I'm worried as well about keeping kids entertained at Aulani, but there is so much to do on the island, especially if your family enjoys outdoor activities.
I had injured my leg and was a bit paranoid about infecting it. I also should have done it sooner in the week when waking up earlier was easier! Oh well 
