I would suggest the Marriott Ihilani. It puts you reasonably close to the airport and it's a good location for the drive to the North Shore.
I'm not sure about the cost, but I would put it in the $200-$250 for the night.
Your other option away from Waikiki is to stay at the Turtle Bay hotel at the North Shore. I'm not sure of the rates - it's no longer a Hilton.