Austin and Dallas are about 182 miles apart by road. Split the difference and you arrive near San Antonio, the city closest to the halfway point between them. That puts roughly 1 hr 50 min of driving on the Austin side and 5 hr 18 min on the Dallas side — the fairest single meeting point among the cities near the middle.
At this range, San Antonio works for a same-day meetup: close enough from both Austin and Dallas to meet for lunch or an afternoon and still be home by evening.
If San Antonio doesn't have what you're after, Houston and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Austin and Dallas.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.