Hi, my wife and I just went to Hawaii for our honeymoon back in February. We spent 2 weeks there: 1 week in Honolulu and 1 week in Maui. It was arguably the best vacation that we had ever taken.
The "volcano" that you are referring to is probably the Diamond Head crater. The mountain is visible from Waikiki beach, and is a nice and gentle 45-50 mins climb to the top.
To kickstart the mood for the trip, I suggest you arrange a Lei (the flowers that Hawaiians wear around their necks) greeting at the airport. I previously assumed that all visitors get a standard Lei greeting, but you need to pre-arrange them.
It goes without saying that Pearl Harbor is a must do. It's rather spine chilling as you walk through the sites, and get a feel of what history and what happened back then.
Since you two are adventurous, I would say definitely check out the North Shore (about an hour drive from Waikiki). There, they offer some of the best waves for surfing. If you don't already know, consider taking surfing classes (Sunset Suratt is by far the best surfing school up there). While you are up there on North Shore, you might want to check out the cage shark diving too.
In Maui, we also did whales watching (might not be in season now), as well as a helicopter ride. Also, be sure to check out a Luau. It may be touristy, but imho no trip to Hawaii is complete without experiencing a Luau.
Here are some pics from our honeymoon for you:
At Pearl Harbor. The ship was left where it was sunk. Depending on the tide level, parts of the ship protrudes from the water surface
Waikiki Beach:
My wife and I scuba diving. It was a first for her!
Shark cage diving:
Galapagos shark:
Horseback riding on the beach:
Surfing lesson at North Shore: