The fair place to meet is Chicago, IL — the city closest to the midpoint of Indianapolis and Kansas City. From the farther side that’s about 8 hr 39 min of driving.
Recommended midpoint
Chicago, IL
From Indianapolis
3 hr 27 min
165 mi to Chicago
From Kansas City
8 hr 39 min
412 mi to Chicago
Indianapolis has the shorter trip; the split is off by about 5 hr 12 min. The alternatives below can even it out. Indianapolis and Kansas City are about 452 miles apart.
Indianapolis and Kansas City are about 452 miles apart by road. Split the difference and you arrive near Chicago, the city closest to the halfway point between them. That puts roughly 3 hr 27 min of driving on the Indianapolis side and 8 hr 39 min on the Kansas City side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Chicago suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Chicago doesn't have what you're after, Louisville and Milwaukee are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Indianapolis and Kansas City.
Chicago is the most populous city in the U.S. state of Illinois and in the Midwestern United States. Located on the western shore of Lake Michigan, it is the third-most populous city in the United States, with a population of 2.74 million at the 2020 census. 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 →
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 →
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.