Yeah I think Airbnb would be a great alternate to expensive luxury hotels. From what I have seen, even some hotels seem to post listing at comparable prices here. Ultimately its really up to you what kind of honeymoon you like. Do you want one where you get room service, and other hotel luxuries at your beck and call, or do you want to be left alone and handle everything yourself. In my view, the best of both worlds would be one of these beach front villas, with a private beach, and hiring a butler for the stay so you don't have to worry about having service.
Sorry for the late reply. I'm going to Sorrento, Italy.
I ended up getting a hotel for very cheap, but i really need to consider the AirBNB idea more. My wife and i werent sure about how much privacy we were going to get amongst other things.
I'd love to hear more about how you would have done something like this. I think i need to learn to be a little more adventurous when it comes to this kind of stuff.