One Island - Nature Oriented = Gotta Be Kauai!
RD - I've been to Hawaii 6 times in my life. Five were business reward trips / 6th was my honeymoon.
To me it's not worth it trying to bounce island to island, you can lose much of a day checking out of your hotel / returning a car / checking in at the airport / flying / getting your luggage back / renting a car / checking into your hotel (or not being able to because it's too early). Anyway, you get my point.
While Maui certainly has some great natural activities, it's also quite built up......would not be a bad trip.
But if you really want a week with Mother Nature, it is Kauai, absolutely no question about it. The southern end has the guaranteed sun, the nice beaches, access to the canyon (an hour drive up to the top and incredible views from the top looking out over the north shore), etc. The ride up northward along the east coast is maybe 90 minutes or so to the hiking (some is very serious hiking) and the zodiac trips. Weather up north can vary, much more exposed to the north Pacific, much more wet and windy. Nightlife pretty much non-existent, but you won't care.
If Hawaii is a one-time trip, you should fly into (or out of) Honolulu and spend at least a day or two there. One day would be Pearl Harbor and Punchbowl National Cemetery up in the mountains overlooking Pearl Harbor and Honolulu. Over 10,000 heroes are buried there, similar to the experience when viewing the Normandy cemeteries. The other day you could circle the island by car, see a few beautiful beaches, see the surfing on the north shore, return south right down the middle of the island stopping for fresh pineapples literally right out of the field, yards from your car.
I'd be happy to help you.....any questions, let me know!