I think that a heliskiing honeymoon was hands down the best thing we could have done for ours. I have talked to a lot of friends, and they all agree that if you are going to be saving up money for a once in a lifetime trip as a couple, that it's really hard to beat a heliskiing trip. My wife and I spent our honeymoon at Silvertip Lodge in BC. The skiing was incredible, and the experience overall is one we will keep forever. I was lucky enough to know about it because I work in the ski industry (that is the spoiler). I wrote this article for my company that details out why I think it's the best honeymoon experience. Feel free to check it out.
It does require that you be skiers, but you don't have to be an expert. That's a common misconception. Both my wife and I are avid skiers, which made it the perfect way to both challenge ourselves and enjoy each other's company doing something we love.
If anyone has other suggestions (we will, of course, take other trips in the future even though it's not a honeymoon) fire away. It would be great to know what other adventure people have done, both personally and for my work.