As a local, I can tell you that if you're planning on a once-in-a-lifetime trip to Hawaii, one week is too short. Each island has its own personality and unique things to see, and each one should take 3-4 days minimum. If you want a taste of each to whet your appetite, then the cruise might be the way to go. If you only have a week and want to cover as much 'ground' as possible without sacrificing quality vacation time and sightseeing, I'd recommend picking two, fly into one, then out from the other and splitting your time between them. Island hopping is time consuming, you easily lose a half day by the time you head from a resort to an airport (which are on the opposite sides of the islands from the airports which are located in the towns where people live and work and don't mind the noise and air pollution), check in, get off the plane and collect your luggage and head to your new resort.
Growing up here I have cousins on two of the islands (Big Island and Oahu), have lived on two (Maui and Oahu), and had relatives with a timeshare on the last (Kauai). Still haven't seen it all (of course I don't spend a lot of my vacation time here either). Kauai and Big Island are the most rural and natural, though they all have spectacular natural vistas to offer. Maui is the best balance between nature and civilization, and Oahu has the most historical sites to visit and civilization, but it is mostly city (except for Aulani and the North Shore).
Aulani is gorgeous and does present a very nice Disneyfied version of Hawaii, and if you want a beach vacation its top notch. However if you're looking for a more Hawaiian/natural experience based on our geological wonders, the Big Island and Maui are probably the way to go.
BTW, "day tripping" to another island in Hawaii really is something best done for business. Not a pleasant experience for a vacation unless you're thinking about launching to Lanai from Maui because that's a quick ferry ride.