If I had 7 days to spend in one Island, I would spend them in Big Island. To get around the Big Island you need a rental car. We were a group of 3 guys and it was a blast. I am sure you can still enjoy the sights and sounds of the big island by yourself too.

I have spend a long weekend in Oahu alone when winter storms in the East coast got my friends stuck at airports. I booked a bunch of tours and met up with people from the tours. I am positive you'll have a good time!

You can find good information for your Big Island trip on the following thread:
http://www.flyertalk.com/forum/hawai...land-trip.html

The helicopter tour of vacation rentals 2 years ago was kind of scam, I would stay away from them; YMMV on these.