When you are limited to a week in the Hawaiian Islands, the best way to see them is one island at a time, or by sea on a cruise, if you are so inclined. In most cases one must fly between islands, which means you will spend a good portion of your day getting to/from the airport, at the airport and flying. Most visitors to Hawaii want to relax, slow down, enjoy the
If you really want to get a flavor of all the islands, think about a cruise. NCL stops in 5 ports, and while you won't get the same in-depth local feel as staying on one island, you get great exposure to a number of islands; good insight for future visits. If you are adventurous and active, consider a 7 day, authentically Hawaiian small ship cruise with Un-Cruise.
Each island is unique and quite different from each other and offer visitors a wide variety of things to see and do. There is something for all types of interests. Hawaii is a beautiful place. Experience it at its fullest - spend as much time as you can on each island, not in the airport.