Thats a tough one!! There is so much to see and do. I was stationed there for almost two years back in the early 90's. I didn't get a chance to see much of the other islands besides Oahu. I did spend some time on Kauai, but it was ravaged by a hurricane so it wasn't as pretty as it normally should have been. I also saw Mauna Loa (volcano) from the air.
On Oahu, the best places to go IMO are, Waimea Falls (best in winter time), Pali Falls (not on a map but easy to get to, let me know if you want directions), Kauai has the best beaches, but on Oahu Waimea Bay probably is the best. Definitely NOT Waikiki. The Arizona Memorial is very moving (at least it was for me).
Haunama (sp) Bay for snorkeling.
For shopping I would go to the International Marketplace in Honolulu. You can find just about anything there.
Hope this helps and have fun. I can't wait to go back.