When you visit Hawaii in October, you can expect the same nice weather and warm ocean as at other months. Actually, it's even nicer than during the hot summer months July and August. September and October are low season months in Hawaii, when plenty of affordable vacation rentals on all the Hawaiian islands are available. Most of the hosts, include all the beach equipment, booggie boards, snorkel gear etc. in their rental fee for free. Kids love to snorkel and boogie board. Make sure they will be safe on the beach and pay attention to beach safety updates.
When deciding for a vacation rental, make sure that the beaches are not far away - rule of thumb though, you pay more for ocean view and much more for ocean front - that's why you and the kids come to Hawaii.
You will have to rent a car on all islands apart from Oahu which has a very well developed bus service at decent rates. When you call the car rental companies, let them give you a quote. Write it all down and compare. October is low season, which is perfect for decent airfares and best car rental rates.
If your kids are over 10, you want to share some adventure in Hawaii with them. The Big Island has some pretty good ones with a live volcano in Hawaii Volcanoes National Park and Mauna Kea summit for stargazing. The Big Island's Kohala Coast (West Coast) has the best Big Island's white sand beaches for the kids and you and the best sunny weather.
Another rule of thumb for all the islands regards the Hawaii weather, east coast has more rain, west coast is drier and sunnier.
Go to the library and get the 'Frommers Hawaii' Guidebook. It's one of the best Hawaii information books about all Hawaiian islands. Hope this will get you going. It's a little big for taking it with your for reference on your Hawaii vacation with your kids. Once you figured out which Hawaii island you want to go visit in October, buy the 'Hawaii Revealed' book for this island. There is a 'Revealed' book for each island with maps, best activities, restaurants, hiking and places to stay. The book is handy and can be taken on your Hawaii road trips when exploring the island of your choice.
Just found out more good news for your October vacation in Hawaii on 'travel specialist' Beat of Hawaii, which prides itself to provide the latest updates on Hawaii travel deals: round trip from Newark to Hawaii for $520 with latest travel 10/27. Seems a fantastic deal to me for travelers from the East Coast to Honolulu Hawaii.