Being a cracker in Japan, hardly a week (day?) goes by without being asked that question, but it’s a natural question given the circumstances, and never asked in malice, just in curiosity (Xenophobes would just ignore me). I ask the same thing to people too - lot’s of people grew up in small towns in the countryside and moved to the bigger cities, but retain their hometown pride.
I know it’s not your situation, but I just give an honest answer and its usually a pretty good conversation starter.
Funnily enough, when I was in Japan it used to bother me less. As a visible foreigner (more or less) I knew I stood out. But in a ‘white’ country like America, it can be more jarring – you just go about your daily life etc until someone points out that you are different and foreign.
pdts
I like this one =)
I heard my goddaughter at the age of 5 say something along the lines of-
My mommy told me the angels brought me down from heaven because she asked for a perfect little girl.
I have also heard someone say
My mommy told me that she found me under a rose petal.
Thanks for the (some more) appropriate (than others) come-backs, guys. 
Yup, it is. It’s not my prerogative in life to educate people, nor to volunteer personal information to complete strangers.
Pdts, your first post’s summarized my issues with the question really well. While it’s usually more like 2-4 times a day than 5 or more, it still gets old, repetitive, and disheartening.
I’m so using that one.
France.
Anything wrong with being honest?
Tell them, “Well, I’m from Dayton, my parents were born in this country, my ethnicity is whatever. To be honest though, as I am so often asked this question, sometimes several times a day, I find it’s beginning to become tiresome. It’s difficult not to find it a little offensive/intrusive when you’re so often asked, because really, what possible difference could it make, to anyone, what my ethnicity is, unless they’re racist or phobic of immigrants? But maybe that’s just me being sensitive.”
Alternatively, just say, “Over there!”, then, when asked where your parents are from, point in another direction and say, “Over there!”
If pressed, I’d say, “My parents were born and raised in this country and are proud to be Americans. That is where they are from, that is where I am from!”
Or you could just be coy, “Where do you think?”, then let them guess. Just keep saying, “Nope, try again!”, “you’re getting warm!”, “not even close!”, “you’re not very good at this, are you?”
And honestly, I think you’re just being sensitive. Y’know, sometimes people just want to identify a, not immediately identifiable, accent. Nothing more.
Is it only complete strangers asking that bothers you?
You’re missing the point of complete strangers not needing to know.
Did try the “Guess” thing before, though! Generally results in 3+ minutes of them not guessing correctly, which is another time sink…
That’s correct.
Examples from yesterday: I’m sitting at the DMV, minding my own business, chit-chatting with a gal from a painting group who happens to be there as well. A random guy from the adjacent row turns around and bluntly asks “Where’s that accent from?”. Not even a hello or anything.
Hubby and I are purchasing groceries and chit-chatting. The check-out clerk asks where we’re from, and proceeds to tell the hubby that he has an accent too. Mind you, he’s born and raised in the US.
I’m not getting the hostility over this question. I spend most of my time living overseas and it was a multiple times daily occurance. I just answer the question. It’s never really bothered me.
What kind of onion did they wear on their belts there and what did they call it?
As someone else said upthread, I don’t think there is a good response. I understand that it is annoying to be asked repeatedly, but it’s also important to realize that each person is, unfortunately, ignorant of how often you get asked those sorts of things. For instance, I don’t have an accent, but my first name, while well known, isn’t terribly common, and matches with a well known TV character that most people my age are familiar with. As such, more often than not, when I meet someone roughly my age, they think they’re clever when they say the catch phrase associated with that character. Yeah, it’s not the same thing, but it also highlights that, from my perspective, it’s annoying because I hear it constantly, but from their perspective, they probably don’t know more than a couple people with that name, so it seems interesting. As such, I’ve tried to learn to be more conscious of those sorts of things and, for instance, will not randomly ask a stranger where they’re from.
That said, the reason that there’s no good answer is precisely because these people have no association. Nothing you say to one will make it any different the next time someone is curious. So, you can either choose to be polite, if very brief, or you can snap back with a clever response and potentially have an unnecessarily negative interaction, and possibly even reinforce some negative stereotypes about wherever you’re from.
Moreso, if you’re actually having some idle chatter with someone, rather than a random stranger butting in, it’s just an unavoidable question. Where such small talk would often include the weather or the price of gas, if there’s something that piques someone interest, it’s likely going to get asked. In your case, it’s your accent, but the same will happen with any number of things, like a particularly unusual hairstyle or hair color, an unusual form of dress, or something that obviously indicates some sort of other topic like association with a sports team. If anything, you should count yourself fortunate to not get stuck to such boring topics as “boy, it sure is hot out today!” and instead will often have the chance in such occassions to either brush it off with a “I’m from wherever” or, if you feel particularly social, actually going on and talking a bit about it.
For instance, I’m obviously in good shape, so I often get asked in idle small talk “How much do you bench?”, and it gets a little annoying sometimes because of how predictable it is, and depending on my mood, I may just give a quick response, or if I can use it as a launch point for a slightly more interesting conversation. It’s a hell of a lot better than the weather conversation, which is ALWAYS boring and never goes in an interesting direction. So, sure, even if it is a bit annoying, consider the alternative.
TLDR: There’s no good answer, so you might as well roll with it.
I’ve moved around a lot, and I usually respond with “Originally, or recently?”
Let’s recap what we have so far:
So here’s my sincere suggestion: Politely say, “I get asked this question constantly and answering gets tiresome. I hope you understand.” And then turn away.
It’s not clear what outcome the OP wants. Why doesn’t she say “None of your business”? It seems that she’s looking for another (seemingly more polite) way of saying the same thing.
I think that you’ve nailed it.
Just acknowledge the question politely, and (as a bonus), smile. 
This question has come up many times on ask metafilter, and a common pattern always emerges in the discussion:
those who are constantly asked the question agree that it is tiresome and invasive
those who don’t get asked the question say something like ‘lighten up!’ or, “I care about accents so I do this all the time and it’s no big deal”
The comparison with an unusual name or notable hair is a good one, I think.
pdts
Yes, there are those who get asked and those who don’t. And, there are those who feel that it is tiresome and invasive vs those who don’t feel it is.
The key difference, though, is how people choose to respond to questions from strangers. You can do and say whatever you want but some choices are wiser than others.
I like the military/embassy/circus brat answer. I use it often. Here in Canada I just say I’m from “Down South”, then follow up that I consider it a birth defect and I don’t like to talk about it - this usually draws a laugh. In Newfoundland I’ll just say I’m a mainlander, and that often ends the inquisition.
Another option is to use a colloquial term for your homeland to stymie the question: Say you’re a Townie or a Bayman*, a Tarheel**, a Scouser***, or that you’re *pure laine * or *de souche . Kama’aina is another good example. These obscure terms should dishearten your interrogator and allow you to make an escape.
*St. John’s NL vs the rest of Newfoundland
**North Carolina
***Liverpool
**** ‘Pure Wool’ and ‘Old Stock’, French and Anglo Quebec.
***** Long time Hawaii resident
I’ll answer, but I don’t love it either. As others have said, it makes me feel foreign, when I am as American, if not more, than the people around me, and grow more so every year. Plus I can’t just say “I’m Indian” because people immediately knee-jerk to “What tribe?” and then I have to go, “No, from India [you dolt]”, so I have to start off with “I was born in India”.
I have an accent that is a mix of all of the places I come from (I presume so, as it’s certainly not upstate NY) but it’s most definitely not an Indian accent. And I don’t have easily definable features - that is, Indian people are not always sure that I am Indian.
Plus, if I don’t think about it, I think “where I am from” is Michigan. Or New York.
But I don’t like silly answers, either, because that just encourages them to ask more.
I have only found one good putdown, though:
say wearily “you haven’t heard of it”, and change the subject. They will immediately feel the urge to say “try me!”. Then say, “ok, (name of small place)”. When it becomes obvious they haven’t heard of it, you can say “see I told you!” and change the subject.
The key is not to act like you are putting them down or disappointed in them, but just breeze over it in passing with a smile. They will feel embarrassed, though, and probably won’t ask any more stupid questions.
And when you name (small place), make sure it is somewhere that someone from your country would have heard of. This means that: (1) you’re not just being a dick for the sake of it; (2) if the person has heard of it, then it is actually someone who knows about your country (ie, they didn’t just “study” abroad there) and you might have an interesting chat.
But really, this is one of the smaller annoyances in life.
To the guy who lives in Japan: what about schoolkids shouting “harro!” at you all the time, or the kids doing ‘surveys’ in Kyoto … gets annoying, doesn’t it? (this may not happen in Tokyo)
pdts
“I’m from the unused part of your brain.”
Really stops 'em dead in their tracks.