I am traveling to Armenia via Moscow from New York. I have an Armenian passport, which doesn't require a visa to enter Russia. Can I go out to the city while on a 6-hour layover? And how will I get back to the transit area when I am back?
Yes, you can exit the transit area by following the signs for the exit and clearing passport control.
To get back to the transit area, just follow the same path as all departing passengers.