Atlanta and New York are about 746 miles apart by road. Split the difference and you arrive near Richmond, the city closest to the halfway point between them. That puts roughly 9 hr 51 min of driving on the Atlanta side and 6 hr on the New York side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Richmond suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Richmond doesn't have what you're after, Raleigh and Washington are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Atlanta and New York.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.