Not too unusual in the Chicago area. I know it as a regional usage. Never heard a white person use it outside this area.
I’m pretty sure we had a thread on this before. Good luck searching under “stay” and “live”. 
I can’t say I’ve noticed whether people I’ve heard say it are one color or another. I hear it a lot on CTA. A news segment the other night was what prompted me to start the thread, when the news did a “man on the street” interview and he said it a couple times. Since it was in regards to neighborhood violence, I wondered whether the language could be part of a cognitive dissonance between being beholden to a neighborhood where one “stays” versus a neighborhood where one “lives.” But if it’s common enough, maybe there isn’t any dissonance between the uses.
Cleveland here, never heard “stay”. But a week ago I was at a bar and chatting idly about sports with the guy sitting a few stools down, and the bartender. The guy turns to me and says, “What’s your home base, mate?” Taken aback somewhat, I figured he was asking about what bar I usually frequented. I managed to stammer, “The Harry Buffalo”. He is probably telling a story about me right now.
Dennis
Alabama. In my experience, I’ve only heard this phrase used by African Americans.
I’m African American and I’ve never used that phrase (nor have I heard it from another Black person), but I’ve heard it from people from India. I’ve assumed it was an Indian English thing.
I’ve only heard people who were down on their luck and didn’t currently have a fixed address say that. They’re staying with family X or friend Y until they’ve worn out their welcome and have to find someone else to crash with for a while.
Or phrased as, “Where you stay at?” Many folks use it (colloquially) where I stay here in the hot, humid, southeast. After being heard for 40+ years, it’s made its way into my phrasebook, too; I’ll toss it out occasionally. No one skips a beat to answer, either. It’s a well-understood term.
I stay to play and go for dough.
Georgia Girl here, born & raised. Heard it all my life, coming from African Americans in my little South Georgia town. That particular one wasn’t something my family adopted, but we knew exactly what was being said. And we didn’t think anything about it, it was just a manner of speaking. There were, however, other words and phrases that were common among everyone of our region that I have to be careful not to use when I travel because people look at me like I am 'flicted. That’s one of them, btw. 
Previous thread about this, from 2013.
Michigan here. “Where do you stay” is black, and has been at least since 1989 when I heard it for the first time.
Full time RV’r here. There are more and more of us these days. Where do you stay is common. We don’t live anywhere.