Houston and Oklahoma City are about 414 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 4 hr 43 min of driving on the Houston side and 4 hr on the Oklahoma City side — the fairest single meeting point among the cities near the middle.
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, Austin and San Antonio are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Oklahoma City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.