Every non-native speaker hates that moment when you've just finished saying something earth-shatteringly important, and your listener says, "Oh cool. So hey, where are you from?" Resist the urge to roll your eyes or walk away. Start with, "Why are you asking?"
No, seriously. One of the biggest complaints I hear during evaluations is that no one has ever given speakers the feedback they want about how they are differently producing certain sounds. Maybe your TH always sounds like a D. Maybe you could focus on differentiating between W and V. Or, a bit more tricky, maybe your vowels sound off.
IMHO, there is no more American-sounding vowel than that "short a" (/æ/). It's a little bit loud ænd almost a little bit nasal. It's forceful and it's clippy, and it's one that a lot of speakers struggle with. And no, I'm not talking about "The Rain in Spain." Check out this clip from the Hæmilton soundtrack, cued up to Lafayette talking about ænarchy. When you're talking about overthrowing the government, you've gotta make sure your æccent is up to snuff.
Here's another clip from a favorite old movie, where Doris so eloquently demonstrates just how nasal this sound cæn be.
Curious how to make this sound? If you hæven't already, click on one of those little /æ/ IPA symbols for a great video on producing the sound. A little tip that I give my clients is that it's mostly produced in the soft palate (thæt place æt the bæck of your mouth where the skin starts to get soft). Visualize it æs a raise in the back of your throat, and keep that tongue braced against your bottom teeth while you do.
Don't worry, nobody thinks you sound like Bill Swerski's Super Fans. The first few times you begin præcticing any new sound it's going to sound a little jarring. One client and I affectionately refer to using the short /æ/ as his "cowboy voice," because he sounds so unapologetically American when using it. In reality, though, he doesn't sound like a cowboy. He sounds like an American English speaker.
So the next time somebody asks you where you're from, seize that opportunity to get some feedback about what tipped them off. And don't forget to use that short æ, "Why are you æsking?"