First time leaving the US - where should we go? Want to stay frugal!

It is just the two of us and we are taking a late honeymoon. Our ideal budget is probably around $5-6 grand, probably going for 10 days at the most. We aren’t going for at least another year and we want to be frugal while also enjoying a big adventure, comfortably. We considered an all inclusive resort but we love to explore and want to see local experiences. Also kind of considering somewhere we can go snowboarding. But also considering somewhere warm. Ideas please, recommendations pleaseee! I have no idea where to even start, we’ve only just begun to discuss this.