A note up front: Hawaii the state includes all of the Hawaiian islands. One of those islands is Hawaii (commonly called the Big Island). The capital of Hawaii (Honolulu) is actually on the island of Oahu. So don't be confused...most of my journal is about Hawaii, the Big Island.
The 'Big Island' of Hawaii was incredible. Once we left Honolulu (on the island of Oahu) we felt like our vacation really began. The Big Island is like visiting a miniature continent. It has among other things the only active volcano in the Hawaiian Islands, snowcapped mountains (with snow skiing believe it or not), tropical rain forests, barren deserts, waterfalls, valleys, beautiful beaches and more. It is incredible driving around the island and seeing the geography change so many times. Rather than stay in one place, we stayed in three different regions for 2-3 days at a time.
My best memories of the Big Island include the green sand beach, the Waipio Valley, the volcano, a luau, and a night at the Dragonfly Ranch.
My best memories of Oahu include the U.S.S. Arizona WWII memorial and the Honolulu marathon (particularly the thousands of supporters who cheered all 26.2 miles).
Quick Tips:
Get off of Oahu and onto the other islands as quickly as possible. I enjoyed a couple of things about Oahu (particularly the backside of the island outside of Honolulu), but the Big Island was what I was really looking for. I have heard similar things from everyone who has been to the Hawaiian Islands (Maui, Kauai and Lanai all sound great as well).
Don't automatically stay at the big resorts. On the big island we found some fantastic (and very romantic) bed and breakfasts. When we ventured into the resort areas we had less fun.
If you can afford it, rent a four-wheel drive vehicle. We couldn't, but we made friends with a couple who rented a Jeep. It was a necessity for certain treks (i.e. driving all the way to the Green Sand Beach and the volcano).Best Way To Get Around:
Rent a car. You will want to see all of the island and the drive is awesome. Also, some of the sights are fairly remote. The last thing you want to do is be stuck on a tour bus for a few hours.