The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Indianapolis and Las Vegas. From the farther side that’s about 20 hr 42 min of driving.
Recommended midpoint
Oklahoma City, OK
From Indianapolis
14 hr 26 min
688 mi to Oklahoma City
From Las Vegas
20 hr 42 min
987 mi to Oklahoma City
Indianapolis has the shorter trip; the split is off by about 6 hr 16 min. The alternatives below can even it out. Indianapolis and Las Vegas are about 1,591 miles apart.
Indianapolis and Las Vegas are about 1,591 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 14 hr 26 min of driving on the Indianapolis side and 20 hr 42 min on the Las Vegas side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Oklahoma City still makes a fair, central place for Indianapolis and Las Vegas to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Denver and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Indianapolis and Las Vegas.
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 →
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 →
Las Vegas, colloquially shortened to Vegas, is the most populous city in the U.S. state of Nevada and the county seat of Clark County. It is the 24th-most populous city in the United States, with 641,903 residents 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.