Honeymoon Planning - Indonesia

Hello!

My fiancé and I are getting married in June and planning our honeymoon for late September/early October for 16 days. We have decided on Indonesia and have started to do some reading on locations (I have a few in mind, such as Sumatra, Java, Flores, or East Nusa Tenggara) but are overwhelmed by options and would love some suggestions. We would love to do 2-3 locations and we want to stay at beautiful hotels while we are there, ideally ones that feel really in nature (skewing away from an excessively modern or huge resort feeling). Our budget is pretty open - I would say we would prefer to stay under $10K (not including flights).

What we love: jungle hiking (hopefully waterfalls), sandy beach time and snorkeling, amazing food, wildlife (monkeys, possibly orangutans, cats, birds, etc.), upscale hotels (especially outdoor showers), renting a scooter, and exploring the area.

What we want to avoid: excessive crowds or big cities, islands that aren't lush and jungly/mountainous.

Thank you in advance for the suggestions. We are really looking forward to hearing. We were thinking of avoiding Bali but if people say we really, really should go to Bali, I think we would prefer to only do a few days on Bali.