Here in the US, no one would guess that I am not American by birth, and I don't really have any regionally distinct accent, so no one has ever asked me these questions. I have, however, had occasion to be the "exotic one".
Long ago, when I was a young naval officer, I was out to dinner with a lovely young woman in Cartegena, Colombia. At the table next to ours was a family with two little girls who kept pointedly looking at me, hiding behind their chairs, laughing with each other and whispering loudly to their parents. My Spanish was nowhere near good enough to eavesdrop, so I asked my companion if she knew why the little girls were laughing at me. "Because you have blue eyes," she said. I was a little surprised that blue eyes would evoke laughter, but then I looked all around the restaurant and, as far as I could see, I was indeed the only one with blue eyes. I found it amusing and understandable.
Later on during that same trip, my friend Tony and I took a couple days off to go skiing in the Chilean Andes. On the way to the ski area, we stopped for breakfast in a truck stop in the back of beyond. As we were eating our eggs, everyone in the kitchen came out just to look at us. They were very friendly to us, but we were clearly an oddity for them.
People the world over are curious.
). I'm from NE Europe, yet I've been mistaken for Italian, Arab, etc. and all that goes with that. I "get" discrimination as I (and my birth family) have often been subject to it. 
