You'll want to do at least some exploring in Hawaii without the kiddos, so you'll need to find at LEAST an occasional babysitter. Date nights without dip spilled on your ONE dress? A run on the beach without telling someone to NOT poke the box jellyfish? Yep, let's figure out some child care options in Hawaii!
My go to for finding babysitters is always going to be going off the recommendations of friends and family. I always do a monitored meet and greet even if they come with a stellar recommendation, just to watch for personality conflicts. We are also somewhat hippie, so like-minded people are helpful (low media exposure, no flashy plastic toys, etc.).
Babysitting trading with my sons' classmates parents, neighbors, and families from churches are also fantastic ways to garner some free or cheap child care in Hawaii. Unfortunately for me, I tend to be busy enough that I find it hard to manage time wise.
A side note, I've never been made to feel like my kids weren't welcome anywhere we've gone in Hawaii. We've taken our kids at very young ages to some very high class restaurants, and even had the chef come give them a tour of the kitchen :) Culturally, Hawaii is a VERY family oriented society!
Side side note: If you're planning on a day of drinking at some North Shore beach during winter, LEAVE THE KIDS WITH A SITTER. You've seen it before, but here it is again: The Pacific Ocean can be ruthless, and it doesn't discriminate. Don't take that chance.
Specific to Hawaii, there is a great FREE referral service for child care. It's called PATCH, or People Attentive To Children. Pop on by and search around. Voted best babysitter referral service!
I have also used the monsters of care.com and sittercity.com, with mixed results. I tend to get lots of responses, very few that follow through, and occasionally find a gem of a person. And by occasionally, I mean once. But in their defense, I really don't use it often, and may not be the best at writing ads.
Some helpful links: