That's a tall order, 4wheelin_again (To avoid tourist areas in Hawaii).

On Oahu:

Rent a B&B in the town of Kailua and hang out at Kailua Beach Park when you are not touring the island. For fun, rent a kayak or wind surfing equipment at this beach. Cisco's in Kailua town is a great place to eat.

On Maui:

Drive around the northwest end of the island for a good thrill and great vistas. Make sure you have a full tank of gas and a cell phone. Drive to the top of Haleakala to see the sun rise. Snorkeling at Molakini, off the island of Maui is a tourist destination, but still a great experience in my opinion. Places to eat are Jaques, in the wind surfing town of Paia, and Penne Pasta in Lahina..

On the Big Island (Hawaii):

There is so much to see and do on this island that you would need more time to do it justice. My advice would be to rent a B&B in the village of Volcano. After exploring Volcanoes National Park, hike the Kilauea Iki crater trail and later, drive down the "Chain of Craters Road" to see the lava flowing at night. Take in the great buffet meals at Volcano House in the park.

There are lots of beautiful hikes on all the islands. If you're into this, buy a hiking book, locally.