That said, I feel compelled to recommend
Blessings and Rituals.
Blessings and Rituals is an excellent piece of writing about the ritual habits of Dwarrows as seen through the eyes of Bilbo Baggins, as well as some of the assumptions about Hobbits made by the big folk. It's rather short, so it doesn't take very much time to work through it, and if you enjoy reading about cultural differences it is an exceptional investment of ones time.
That said, with this being my first rec, well, period, I'll admit that while I find it to be one of the Best Damn Fics I've ever read, I've been a Tolkien fanatic since I was a child and interactions between cultures fascinate me, so I have a bit of bias.
In the same vein, I might as well recommend
Ransom.
This story is told through the eyes of Hakim, a man native to the deserts of Harad who hopes to ransom his only son back from the Gondorians after the War of the Ring. While waiting for an audience with the new King Elessar, Hakim thinks back to his childhood when his own family held a Gondorian soldier for ransom, and the events surrounding him.
Ransom is another work I am extremely enamored with, but since it too is set in the world of Tolkien and focuses around a clashing of cultures between different peoples, the same bias I expressed regarding Blessings and Rituals is also present here.