End of September – Private? Maybe a beach?

I've been trying to plan our honeymoon for the end of this September through the beginning of October. We'll probably do ten days on this trip.

After the past year and the wedding and the planning, and the…everything, when we talk about what we want to do the word that keeps coming up is "private". We intend to leave the wedding and for the next ten days if we interacted only with food servers and hotel clerks that'd be fine. We don't need clubs, nightlife, to see or be seen, music, anything. We want good food and quiet. We'd like nice scenery–a beach, an ocean, a mountain, trees, birds, any of those.

My fiancee is a warm weather beach person so I've been looking for a private over-water villa we can hole up in. Bora Bora or Papeete. Or Bali. The options are overwhelming. That's also a long flight from the U.S. in either direction for only ten days. I started looking at Costa Rica–maybe an AirBnB somewhere near a remote beach–and Panama, but I'm a city guy and am out of my depth there, too.

I'm hoping someone here loves those private, over-water villas with a private pool that opens up onto the ocean, and knows where the best of those are. Or a quiet beach, or a remote AirBnB in the mountain rainforest in Costa Rica somewhere. Hell, even a nice hotel in New England and we could watch the leaves turn if it's pleasant and quiet.

We'd like decent restaurants but we're also good cooks and don't mind buying and cooking the food. We can get by in French and Spanish but also don't mind gesturing and miming and smiling a lot and getting along with the locals.

Neither of us think we need to blow up a budget to have a good time, but it's her (and mine, really) honeymoon and I don't mind spending for a nice time. The rates for those overwater villas in Bora Bora aren't out of the question, it's more I was wondering if after we did it someone would pop up and say, "yeah, those are great, but you should have tried 'this' instead." I also have millions of Hilton Honors points. Three or four million, I think. I've never used them.

I know that's way too open ended to get great answers, so mostly I'm hoping you guys can help me narrow my search. Late September, quiet, private, secluded, either good restaurants or grocery stores available, and I know she'd love it if it were warm. We can fly as far as we need to to get it, but we also aren't looking to brag or Instagram about it.

Any tips or advice gratefully accepted.