Austin and Oklahoma City are about 360 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That splits the trip almost evenly — about 3 hr 49 min from Austin and 4 hr from Oklahoma City.
That's a half-day drive from each side, so Dallas suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Dallas doesn't have what you're after, San Antonio and Houston are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Austin and Oklahoma City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.