I would completely skip Oahu and Waikiki (too crowded). If you do end up on Oahu, Lanikai beach is not to be missed.
I would probably do 4 days on Maui and 3 days on Kauai to get a good taste of the Islands.
My favorite island is actually the Big Island (Hawaii). You see all sort of things not present on the other islands; however it is the least appealing for most tourists. It is quite large and there is plenty to do, but it is not an exciting scene at all. If fine dining is important to you, stick to Maui or Oahu. If you do end up on the Big Island, ask a local how to get to "Two Steps" -- it's an awesome snorkeling spot near the Point of Refuge park. A hike down in Waipio Valley is also beautiful. Of course you can't miss the active volcano down at Volcano National Park.
On Kauai, take a Zodiac boat up the Napali Coast.
On Maui, take a trip to Hana (ideally take a tour that drives you one way and flies you home by helicopter). You can drive the road to Hana yourself cheaper, but it is a long day trip. Stop at the hidden beaches along the way. I enjoyed the bike ride down Haleakula Volcano (I'm sure I am messing up on the spelling). Maui has the best beaches of all the islands. It is quite expensive and has great restaurants and golf courses.
You could easily enjoy any single island for the whole trip, but I think that 3-4 days on two different islands will be nicer on your first trip. Most people discover that they enjoy one island better than all the others, but it's hard to predict which one.
Enjoy!