My husband and I did Oahu and BI with 11 nights flying from Syracuse NY. @ islands is doable with 10 nights. Fly into Honolulu and stay 2 nights in Waikiki. Book a Pearl Harbor Tour while staying in Waikiki. Fly over to the BI and stay 5 nights.We stayed in Kona and drove all over the BI including VNP in 5 days. Fly back to Honolulu and spend the next 3 days exploring the island of Oahu with a rental car. Go to the North Shore and have a shrimp plate lunch :-)
That's my advice anyway.
BJ's also has good car rental rates if you are a member.