What should a honeymoon entail?

Apologies if this thread exists already and I didn't dig far enough!

My wife and I tied the knot in May and have said we'd like to go to NZ for a month for our honeymoon. We're typically quite lax on holiday plans but do like to be romantic so I figured this would be a great place to turn to to make sure I'm not missing anything when it comes to honeymooning vs. a regular vacation. What kind of activities/itinerary should we consider? If anyone has spent time in Auckland and Christchurch on a honeymoon and has some suggestions please let me know!