Just got back from the big island and have yet to find anywhere to buggy. The old airport in Kona is a park now but not open to buggies. Beaches are small and full of people so that's out.
Kawai is the same, sand is to soft and not enough beach.
Any other ideas, besides Kiteboarding?

get in the water .... its easier on the ribs

Hawaii is composed of volcanic peaks surrounded by coral reefs. Finding large areas of flat land not already gobbled up by a millionaire developer is gonna be tough. Even the old pineapple / sugar cane fields are being developed as new housing areas.

Other suggestions:

Hiking - As crowded as the islands are, hiking is one of the lesser known and utilized activities there. Some of the trails will take you to areas rarely visited by anyone, including protected areas where non-native plants haven't taken over. Careful what you leave in your car, the parking lots are notorious for break-ins.

Surfing - Hawaii's still the number one spot on the planet for surfing. Of the islands, Oahu reigns supreme for good surf spots, but all the islands have good surfing (even Molokai and Lanai).

Sailing - Some of the best (and challenging) sailing on the planet can also be had in Hawaii. Conditions range from protected waters like Kaneohe Bay on Oahu to "Cape Horn" like conditions in the Alenuihaha Channel between Big Island and Maui.

And it's spelt Kauai for your info.