The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of El Paso and Indianapolis. From the farther side that’s about 14 hr 26 min of driving.
Recommended midpoint
Oklahoma City, OK
From El Paso
12 hr 4 min
576 mi to Oklahoma City
From Indianapolis
14 hr 26 min
688 mi to Oklahoma City
El Paso has the shorter trip; the split is off by about 2 hr 22 min. The alternatives below can even it out. El Paso and Indianapolis are about 1,263 miles apart.
El Paso and Indianapolis are about 1,263 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 12 hr 4 min of driving on the El Paso side and 14 hr 26 min on the Indianapolis 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 El Paso and Indianapolis to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Dallas and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between El Paso and Indianapolis.
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 →
El Paso is a city in and the county seat of El Paso County, Texas, United States. It is the 22nd-most populous city in the U.S., sixth-most populous city in Texas, and the most populous city in West Texas with a population of 678,815 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 →
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.