The North Shore is quite a drive from all the attractions - at least an hour, hour and a half depending on where you stay. Keep in mind that the northeast shore of Oahu is substantially wetter and cooler than the south (Waikiki and Honolulu) by about 10 degrees. If you want beaches and activity, stay in Waikiki otherwise you'll spend most of your day commuting.

If you want want quieter but still have access to activities, you may want to consider staying on Maui instead. There are a lot of nice quiet resort areas close to Lahania -- Kahana and Honokowai come to mind - probably a 5 to 10 minute drive to all of the activities in Lahaina. There's a lot to do there, and not as crazy as Oahu.

The attractions you mention, plus renounced and not-to-be-missed protected snorkling spot Hanauma Bay, are located in or near Waikiki on the south eastern end of Oahu. Depending on where you stay on the North Shore, which is north west of Waikiki, you'd be about an hour or more drive from Waikiki and its attractions.

A better bet would be Kailua, which is about 30 minutes drive north of Waikiki (if you avoid rush hour), on the other side of the Koolau mountain range that cuts through the island. Additionally, Kailua Beach is a great family friendly beach with activities/gear such as kayaking and windsurfing as well as snorkling. From Kailua you could also readily access the North Shore and its surroundings, within 30-40 minutes.