I definitely recommend Priscilla and Cino's place. It has everything you need for a comfortable stay for as long as you need. I'll just note that the power went out a couple times while we were there, but they provided a lantern and a flashlight and we were fine. We also had the turtle Bay resort lobby nearby where we could get coffee and access the internet.
As far as staying in the north shore goes, this is where you want to stay. Oh and definitely check out Ted's bakery less than a ten minute drive away and the Polynesian Cultural Centre which was a lot of fun! Our daughter got to be in a luau.