We traveled to Oahu last summer for a week. I have only a few budget tips since we had a free place to stay with family. We bought our airfare outright and seemed to get a good price.
We did rent a car and we rented through:
http://www.discounthawaiicarrental.com/
We ended up with a car from Alamo, which is probably one of the cheaper rental places near the airport. It is slightly off-site from the airport so you have to take a shuttle there. We requested a compact and were able to pick from what was available on the lot.

We were excited to have an Altima for the week. I definitely recommend having a car.
We went to the luau,
http://www.paradisecoveluau.org/ right next to Aulani. It is truly out there, not much around. So my only experience with Aulani is driving by it.
I definitely recommend this place:
http://www.hawaiiansurfadventures.com/
They do surf lessons but we did a canoe tour and it was awesome! Hanauma Bay is close by.
http://www.hanaumabaystatepark.com/
And if you decide to do Pearl Harbor be sure to get the free tickets on their website EARLY. I don't know how early they give them out, maybe 2 or 3 months. We didn't end up getting any tickets to go out to see the memorial. We did go to the visitor center and there was plenty to see.
That doesn't help you with your budget trip to Aulani, but if you are going to travel all the way to Hawaii you may want to see some sites! And most of them aren't right near Aulani.