The genuinely unique experiences in any country cluster in a few categories worth hunting deliberately. There are the geographic one-offs: a natural phenomenon, landscape, or wildlife that exists nowhere else, which the national parks service or UNESCO listings will point you to. There are the living traditions: a craft, ceremony, performance art, or sporting event that the culture itself invented and still practises, best experienced at its source rather than in a staged show.
Then there are the everyday rituals that feel unremarkable to locals and extraordinary to everyone else: a bathing culture, a tea or coffee ceremony, a particular way of eating, a festival with no equivalent abroad. These are often what you talk about years later, more than any monument.
To find them, ask locals what they miss most when they travel abroad, and search for what the country holds recognised cultural heritage status for. Book rare experiences well ahead, go with a local guide where context matters, and participate rather than just photograph; that is the difference.