I've been fortunate to have been there many times - In my opinion, one week (7 days) is not enough time, due to flying/flight there (ti cost a bunch and takes a whole day to get there - at least from Mn). 7 days would be ok for one Island, but not enough time to really experience the Island/native culture of that Island. 2 weeks would give you a great experience and visits 2 Islands. For a first timer to Hawaii, you almost have to go to Oahu (Waikiki/Honolulu) as others have suggested, need to experience Pearl Harbor. You can spend a whole day there, maybe even two seeing all that goes with and is around the harbor. I'd recommend staying on the south east side of Waikiki tourist area, by the park/zoo. Last were were there, it was quieter and seemed less like "downtown" due to open park space. The aquarium is on that side, that isn't too bad of a walk from hotels in that district. I'd recommend diamond head state park, it is quite the hike to the top, but well worth it. No need to rent a car on Oahu, if you need a car, rent it for the day from one of the hotels in Waikiki. City tour is great, lots and lots of culture / history to explore. Island tour is worth it and can do on your own with a one day car rental. Google all the other great things to do and see on Oahu.

The second island is hard, as the other three islands are totally different then Oahu - I'd likely recommend Maui or Kauai. (I hate to recommend Kauai, as it's a Jewel and the less people that know about it the better (tourist can't spoil it then). You will need a car rental on any of the other islands to get around and sight see. There are tons and tons of activities on the Islands. What ever fits your interests. Google is your friend. On Kauai, I'd recommend staying in Kapa`a (central location to see all the island, good food with in walking distance of the hotels/rentals. On Maui, I'd recommend staying in the Kaanapali area. All the Islands are vehicle friendly - hard to get lost on (only one main road for the whole island) and pretty laid back/slow paced. Take in the culture and history, it's great! Google is your friend for finding your interests to explore.