The fair place to meet is Kansas City, MO — the city closest to the midpoint of Indianapolis and Oklahoma City. From the farther side that’s about 9 hr 28 min of driving.
Recommended midpoint
Kansas City, MO
From Indianapolis
9 hr 28 min
452 mi to Kansas City
From Oklahoma City
6 hr 15 min
298 mi to Kansas City
Oklahoma City has the shorter trip; the split is off by about 3 hr 13 min. The alternatives below can even it out. Indianapolis and Oklahoma City are about 688 miles apart.
Indianapolis and Oklahoma City are about 688 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 9 hr 28 min of driving on the Indianapolis side and 6 hr 15 min 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 Kansas 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 Kansas City doesn't have what you're after, Memphis and Nashville are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Indianapolis and Oklahoma City.
Kansas City, abbreviated KC or KCMO, is the largest city in the U.S. state of Missouri by both population and area. It is located on the Missouri River at its confluence with the Kansas River, within Jackson, Clay, Platte and Cass counties. Read more →
Indianapolis, colloquially known as Indy, is the capital and most populous city of the U.S. state of Indiana and the county seat of Marion County. Indianapolis is situated in the state's central till plain region along the west fork of the White River. Read more →
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 →
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.