Montauk itself is pretty bare as there are not many trees, mostly dunes . There are hiking trails, surfing beaches, but you need a car to get to any of those.
Hotels in Montauk are of three types:
- those who cater to young party goers (very barebones, motel-like)
- those who cater to hipsters (same as above, but better decoration and more expensive). Surf Lodge or Rushmeyers
- those who cater to families
None of these strike me as a particularly good honeymoon kind of place. Perhaps the hipster ones if you can afford.
You may want to look instead at B&B's in East Hampton. Maidstone Arms comes to mind, but there are several others. They will be a lot cosier (typically century old houses), you will be in a cute town, some will lend you a bike, there will be nice restaurants nearby. And if you want to get to Montauk, it is only a 20 minutes drive.
To clarify, Montauk is indeed technically part of East Hampton (as are amagansett, wainscott, and part of sag harbor). Living in Montauk you pay taxes to East hampton town, and your streets are patrolled by the east hampton police. Parking at the beach requires you to have an east hampton parking sticker. Yes, for a long time, this village was less fancy than the others, as it was harder to reach, but this is changing fast with the hipsters that started coming in in the last few years. Now it is really Williamsburg East. It is about 15 mile drive from east hampton village to Montauk village.