Where can we go that’s a “non typical” honeymoon?

So my wife and I got married almost two years ago, but haven’t had our honeymoon due to life and finances. We are looking to go sometime during 2026.

We live close to Saint Louis Missouri and have about 5k MAX to spend for a week. Ideally around 3k but could stretch if it made sense.

We’re not big drinkers, our main focus would be to relax but we also want a few activities.

We go back and forth on if we want to do a beach honeymoon or not, my work takes us to playa del Carmen every year and we definitely don’t feel like we have to do the beach for a vacation. Obviously if we wanted to do beach we could go pretty much anywhere in Mexico, Costa Rica, etc

We honestly want a pretty private area, so all inclusive are probably off the table. My idea was something like renting a cabin in Gatlinburg for a week so we could get away from all the tourist but still have plenty to do pretty close by if we got bored.

If we wanted to do the beach, i thought about just renting an Airbnb in Puerto Rico, Cancun, etc.

We’re pretty much open to anywhere as long as we can have some true privacy without 4000 other people around us at all times.

What are some places that are kind of unheard of for a honeymoon like this? Also, we’re open to international if there’s something similar to gatlinburg elsewhere.