My native country is the US, born outside Cleveland, raised in a suburb of Chicago, schooled in Tennessee, and lived with my own family near Seattle. While I've traveled internationally a lot, I've only spent the majority of my time outside the US during the past three years, first in England, then in the Netherlands. Currently, I'm a US citizen/ Dutch resident (happy with both: hence my delight at the "Welcome Home" greeting that Dutch immigration gives me now).
On the road, though, I try to keep a low profile with regard to sporting any nationality. In line with safety guidance, I avoid logo shirts or symbols that might suggest any particular origin: I don't generally volunteer where I'm from, or where I'm going. If someone in Europe asks, I'm pretty open: either "From Seattle" (a nice, distant, liberal spot that few people are even sure lies within the continental US) or "Living in the Netherlands" (a nice, local, liberal spot that certainly lies beyond any US influence).
Sometimes though, as in the bazaars in Istanbul, the "From Seattle" answer simply raises eyebrows (and prices) when they recognize that I'm an American. So, when in doubt or uncomfortable, I've always adopted the easy subterfuge that I was from Canada (a nice, distant, easy-going spot that everyone seems to like). I've been to Vancouver enough to carry a conversation, and the accents are generally indistinguishable (throw in a 'eh now and again, and you're there...)
But, most recently in Jerusalem, when I said I was "from the Netherlands", I noticed that I got an even better response than when I feigned a Canadian accent. The merchants immediately seemed to adapt a less aggressive approach (or moved on to the next victim entirely), in contrast to a couple of shops where I offered up Seattle. A couple of merchants tossed me a few lines in Dutch, but, since mine was (incredibly) better than theirs, the illusion held. My Dutch driver's license and bank card sealed the deal.
I'm always struck by how people react differently to others based on their origin: my observation is that the Dutch do enjoy a good international reputation when they travel abroad. Hopefully, the US can regain a similar perception some day. Meanwhile, I only play this card in anonymous, harmless situations where I'm avoiding a hassle, but 'going Dutch' is clearly better than being Canadian.
Now if I could just add a few inches and regain my hair color...