We're staying at the Westin Princeville in November, which will be a new resort for us.
Our favorite resort is the Hanalei Bay Resort on the North shore. The views are amazing, they have a golf cart that will take you to the beach if you don't want to walk down to the beach or back up to the resort, and a great pool. Every one of our family and friends we've recommended Hanalei Bay Resort to has also loved it. We're staying at the Westin instead of HBR because we are Marriott VC members so we're staying on points.
The North Shore is absolutely stunning. I highly suggest taking a Na Pali Coast tour while there.
If you want a central location, Marriott's Beach Club on Kalapaki Beach is also a great choice. Marriott still owns the vacation club portion of the resort, but the hotel portion is now the Royal Sonesta Kauai Resort. The pool is huge. The Kalapaki Beach, as well as Hanalei Bar, are both great beaches for families. The water is calm, and the beaches are very large and not as crowded as the Poipu area.