One of the best things about life in Hawaii is the focus on family. Wherever you go in the islands, kids are both seen and heard. They are treasured, integral ribbons in the weave of everyday life. It begins when parents plan the luau celebrating the child's first birthday; later, those same parents will be sweet-talking the neighbors to get flowers they can use to sew leis for their kids' high school graduation ceremonies.
Of course, between the above-mentioned milestones of family life, there are countless days at the beach, early mornings spent packing lunches and searching out extra socks for hikes, and visits to places that are both fun and (shh!) educational. All of which can be enjoyed by a family from the continental U.S. that's on vacation, if they know where to look. 
When I was growing up on Oahu, we visited Bishop Museum to marvel at its treasures, starting with ancient history and continuing up through the monarchy. We went to the oceanfront Waikiki Aquarium for glimpses of the creatures that inhabit the waters around us, hiked to the lip of Diamond Head to check out military fortifications and sweeping views, and spent time at the Arizona Memorial visitor center. We also rode the launch to the serene memorial to learn the lessons of World War II.
For the most part, our pleasures were simpler, and even today, people who want to explore Hawaii's natural beauty at a leisurely pace can do so. Then, as now, all beaches were public in Hawaii to the high-tide mark. In addition, both as a territory and later as a state, Hawaii focused on developing a comprehensive network of federal, state and municipal parks. In most cases, access is free, and when there is a charge, it is nominal.
These stalwarts remain, but on Oahu and elsewhere, there has been a steady growth in attractions and activities that are suitable for the whole family. In addition, Hawaii residents are busily working to preserve the state's multicultural heritage. Historical gems include Iolani Palace and the Queen Emma Summer Palace in Honolulu and Hulihee Palace in Kailua-Kona on the Big Island. There also are museums ranging from simple to elaborate, each with a focus that generally will appeal to families. 
Heritage Lines
Other places that have been important since ancient times—whether for religion, aquaculture or as places of refuge—are preserved and in most cases are open to visitors. Another exciting trend that's been blossoming in recent years is the creation of guided adventures that take place on private land.
Visitor interest in everything from all-terrain vehicle tours to horseback rides has led to the designing of half-day and full-day adventures that combine elements of history, heritage, culture, agriculture and even botany and volcanology into immersive experiences that resonate with both kids and adults.
People may chuckle about the magnetic pull that horses seem to have for preteen girls, but I say it's more on the order of earthly magic. Years ago, one of my kids rode a retired polo pony through a docile herd of cows in upcountry Maui. She thought she was learning to ride, and helping socialize the cows to the presence of people and horses. She was, but she was also absorbing the stories shared by a fifth-generation paniolo (cowboy). She took experiences such as this to heart and now volunteers as a camp staffer working with younger kids.
My other daughter's first horseback ride was quite different, but equally memorable. She learned the basics of "horse whispering" before helping saddle up. That, and such experiences as an earlier dolphin-interaction class, gave her the confidence to believe she could achieve her dream of working with animals as a veterinarian. 
We've been lucky enough to create other family memories where the generational boundaries blurred and the only duty was to have fun. We've gone for hikes, stopped off for fresh chow fun to munch on in Chinatown while buying blooming crab claw narcissus for New Year's, taken the family kayak to Kailua Beach Park and been surprised by honu (Hawaiian green sea turtles) rising to the surface to gaze at us, and tagged along one day on an ecotourism exploration led by one of my high school classmates.
On such tours, we've squelched through mud to see low-lying terraces farmers made to cultivate taro— terraces so skillfully made they've survived for centuries. We've also hiked mountain paths and seen stretches of a historic cobblestone mule path. 
And we've floated down canals created a hundred and more years ago to irrigate some of the sugar plantations that used to blanket parts of the islands. Speaking of those canals, the guide on one of those adventures shared stories of how when he was a kid, he and his friends used to have to sneak into the area so they wouldn't get in trouble with the grown-ups. He thought it was pretty cool that now he gets paid to take people there. So did we.