Good advice from Andre.
Lorie and I were there from 83-86; stationed at MCAS Kaneohe Bay. Don't know how the Marine Corps outsmarted the Navy, but we traded Barbers Point for KBay after WWII. Wonderful place and definately the "right" side of the island. That said, we were there about 30 months and I was ready to leave (and since Lorie was 8 months pregnant she was too!). Even though I spent about 12 months deployed to various places, Hawaii lost its appeal after a while - I think it was the "sameness" every day. No seasons..... I didn't have a bike back then, but if I did I think I would have gone nuts!! As someone else here said, after one or two day trips, you're done! I would second the suggestion for a dual-sport bike. Maybe you can run around the Kahokoos (sp?) - just be careful you don't run across any "secret "Mary Juana" plots - no joke.
If you can, take trips to the other islands. Molokai is good. Hawaii is ok - used to deploy to the Pahokola Trng Area; 6k ft altitude and beautifully situated between the 2 mountains. Kilawea (sp) is just over the hill and makes a beautiful scene when it erupts! And finally, Kauai is a beautiful place. Oh yeah, Hawaii is where I got my diving license and it's a great place to dive! You can see for miles and the water is relatively warm. On the side of Diamond Head there used to me (may be closed) an Army club - The Cannon Club - that had great Sunday brunches and great views. You can also get cottages at KBay that are on the bay, great places and you really should look into them. Bellows AFB also has cottages, etc that are right on the beach. Magnum PI used to film down there quite a bit.me)
And always remember, the Geckos (no, not from Geico) that are crawling on your walls are in fact your friend (they eat the roaches and other critters fond of warm, humid climates. This is bringing back wonderful memories! Hawaii is where Lorie used to put almost everything we owned into plastic bags - especially food - good tip to remember! Your side of the island might be more civilized, but I wouldn't count on it.
All in all I'd have to say I did enjoy Hawaii for the time I was there. I was with my beautiful wife, young son, manufactured my future daughter, beautiful weather (except that one New Year's day we had to put on sweatshirts; what a horrible day!).
The roads from the windward to the leeward (Honolulu) are as I understand it, much better than they were in my day (Likelike and Pali Hgwy) - might be feasible for you to live on the windward side - in my humble opinion the better side to live.
All that said, good luck and enjoy the time with your family!