On Oahu, visit the Polynesian Cultural Center, on Maui, try one of the tours up to Haleakala, on the Big Island, you've got to visit Kilauea Volcanoes National Park. There have been ongoing eruptions since the 60's, some of them quite spectacular. The Kona side has evolved into a miniature Waikiki but Waimea has kept some of the old ways in spite of the huge influx of mainlanders into the area. Honokaa is a place where they still have wooden sidewalks and hitching posts for your horse. There are a number of nice old
villages from the sugar plantation days, on the Hamakua Coast as well as the
Ka'u side.
I would recomend a nite or two stay at the Volcano House. It's an old hotel restaurant built on the rim of Kilauea Volcano. The steam bath/sauna is heated by the Volcano, the restaurant is very nice and the food is pretty good.
Hilo is a mix of some old and some new, you just have to find the old.
Hope your honeymoon is truly memorable.
Ainokea