I have thought for a while now that Japan and Germany would be fun and unique honeymoon locations. Both places have a lot of old history, from castles to temples, ruins to memorials.
I lived in Japan when I was younger, and trust me, if your daughter is an adventurer, Japan has more than enough to satisfy! There are spelunking tours, haunted hiking trails, and more jungles than you can shake a stick at. Plus, Mt. Fuji! I believe you can climb it for free, my mother did it a long time ago and the people living in the temples there gave her a decorated climbing stick which she got to keep.
I've never been to Germany, but if it's mountains you want, look no further! It is a beautiful place with old villages and picturesque forests. The Disney princess in me really wants to check out the Neuschwanstein castle.