The fair place to meet is Columbus, OH — the city closest to the midpoint of Detroit and Indianapolis. From the farther side that’s about 3 hr 31 min of driving.
Recommended midpoint
Columbus, OH
From Detroit
3 hr 26 min
164 mi to Columbus
From Indianapolis
3 hr 31 min
168 mi to Columbus
That’s an even split — both sides drive within 5 min of each other. Detroit and Indianapolis are about 240 miles apart.
Detroit and Indianapolis are about 240 miles apart by road. Split the difference and you arrive near Columbus, the city closest to the halfway point between them. That splits the trip almost evenly — about 3 hr 26 min from Detroit and 3 hr 31 min from Indianapolis.
At this range, Columbus works for a same-day meetup: close enough from both Detroit and Indianapolis to meet for lunch or an afternoon and still be home by evening.
If Columbus doesn't have what you're after, Cincinnati and Cleveland are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Detroit and Indianapolis.
Columbus is the capital and most populous city of the U.S. state of Ohio. With a population of 905,748 at the 2020 census, it is the 14th-most populous city in the U.S., second-most populous city in the Midwest, and third-most populous U.S. state capital. Read more →
Detroit is the most populous city in the U.S. state of Michigan. It is situated on the bank of the Detroit River across from the Canadian city of Windsor, Ontario. It is the 26th-most populous city in the United States and the largest U.S. 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 →
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.