How many days do you have? Big Island needs more time that Maui or Kauai, and can you be more specific about activites, like hiking, fishing, eating good food, history, nightlife, shopping, etc. as your question is a little vague, sorry. I would not go to the Big Island with less than 7-10 days, it takes a LOT of driving? How well do your children cope with long drives? More info will help folks help you. Thanks.

thanks for the tip jamie99. our kids are terrific in the car so no worries there - we would like to see a volcano, attend a luau, hiking would be nice. i guess the main thing would be the water (snorkeling, kayaking, taking surf lessons, etc.) and pool play. Shopping is not a big priority. We are planning to stay 2 weeks in hawaii.

thanks for any info you can supply.

The Haleakala crater on Maui is spectacular and colorful; but for a live volcano, it has to be the Big Island, and right now you can see venting from the top, Halemaumau crater. (https://www.google.com/search?q=halemaumau+crater+overlook&hl=en&client=firefox-a&hs=Ni8&tbo=u&rls=org.mozilla:en-US:official&tbm=isch&source=univ&sa=X&ei=dsLxUJe4CoXaqgHnpYGIDA&ved=0CDsQsAQ&biw=1138&bih=939). While at the Volcanoes National Park, the kids would love the walk through the Thurston Lava Tube, and the drive down to the coast (Chain of Craters road) is beautiful, and you can view a sea arch at the bottom. Near Hilo is a beautiful little free botanic gardens/zoo: http://www.hilozoo.com/, and there's also a state park where you can climb into a huge lave tube system (Kaumana Cave: but you will just stay in the first 100 feet, probably (some great old grafitti carvings inside). Also the waterfalls in Hilo, and Lava Tree State park are worth visiting.
The drive to the west coast will be ~3 hours, and that's where you find the nice beaches. I like the Waikoloa resort area (this condo is great, 2b/2b, near A-bay, which has great swimming, very nice snorkeling, etc.; http://www.vrbo.com/413069). There are great petroglyphs parks in Waikoloa and in Puako (next to the Fairmont). From there, it's a 10-15 minute drive to other fabulous beaches on the Kohala coast. The state and national parks and monuments on the Kohala coast are great, too, like heiaus, ancient fishing villages (Lapakahi State Historical Park, etc.) (http://www.nps.gov/puhe/index.htm)
There's a LOT to do and see on the BI!

I just checked another forum and the hike to the currently live lava at Kalapana takes just under 2.5 miles each way, not sure if the six year old could handle it. It is supposed to be a very tough hike over some rough ground, and need hiking shoes not tennies, that lava is sharp. You could always take a helicopter ride, also I have read that you can see the glow at night from the Jagger Museum there at VNP, not sure if the glow would satisfy,kind of up to the OP.

Best snorkeling would be Big Island or Maui
Best surfing would be Oahu
Best hiking would be Kauai or Big Island
Best kayaking would be Kauai (only island with navigable rivers)
Best luau would be Maui probably

So Mary, they all 3 have some of what you are looking for.

I didn't see that the Kalapana hike was mentioned; I wouldn't think that it was even worth doing right now, there's no active lava flow.
The venting from the crater, however, is very cool; always amazes me, along with the other volcanic features close by (the gas/steam rising from the ground, the smell, etc.)
Kayaking in Kealakekua Bay (Captain Cook) on the Big Island is still possible, but the licenses have been much curtailed. (I presume you meant ocean kayaking?)