The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Houston and Omaha. From the farther side that’s about 8 hr 40 min of driving.
Recommended midpoint
Oklahoma City, OK
From Houston
8 hr 40 min
414 mi to Oklahoma City
From Omaha
8 hr 35 min
409 mi to Oklahoma City
That’s an even split — both sides drive within 5 min of each other. Houston and Omaha are about 795 miles apart.
Houston and Omaha are about 795 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That splits the trip almost evenly — about 8 hr 40 min from Houston and 8 hr 35 min from Omaha.
That's a half-day drive from each side, so Oklahoma City suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Oklahoma City doesn't have what you're after, Dallas and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Omaha.
Oklahoma City, often shortened to OKC, is the capital and most populous city in the U.S. state of Oklahoma. It is the 21st-most populous U.S. city and 8th largest in the Southern United States, with a population of 681,054 at the 2020 census. Read more →
Houston is the most populous city in the U.S. state of Texas and the Southern United States. It is the fourth-most populous city in the United States, with a population of 2.3 million at the 2020 census. Read more →
Omaha is the most populous city in the U.S. state of Nebraska. It is located in the Midwestern United States along the Missouri River, about 10 mi (15 km) north of the mouth of the Platte River. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.