The fair place to meet is Denver, CO — the city closest to the midpoint of Indianapolis and Los Angeles. From the farther side that’s about 20 hr 56 min of driving.
Recommended midpoint
Denver, CO
From Indianapolis
20 hr 56 min
999 mi to Denver
From Los Angeles
17 hr 24 min
830 mi to Denver
Los Angeles has the shorter trip; the split is off by about 3 hr 32 min. The alternatives below can even it out. Indianapolis and Los Angeles are about 1,806 miles apart.
Indianapolis and Los Angeles are about 1,806 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 20 hr 56 min of driving on the Indianapolis side and 17 hr 24 min on the Los Angeles 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. Denver still makes a fair, central place for Indianapolis and Los Angeles to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Albuquerque and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Indianapolis and Los Angeles.
Denver is the capital and most populous city of the U.S. state of Colorado. Officially a consolidated city and county, it is located in the South Platte River valley on the western edge of the High Plains, and is just east of the Front Range of the Rocky… 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 →
Los Angeles (LA) is the most populous city in the U.S. state of California, and the commercial, financial, and cultural center of Southern California. 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.