The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Denver and New Orleans. From the farther side that’s about 12 hr 5 min of driving.
Recommended midpoint
Oklahoma City, OK
From Denver
10 hr 34 min
504 mi to Oklahoma City
From New Orleans
12 hr 5 min
576 mi to Oklahoma City
Denver has the shorter trip; the split is off by about 1 hr 31 min. The alternatives below can even it out. Denver and New Orleans are about 1,080 miles apart.
Denver and New Orleans are about 1,080 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 10 hr 34 min of driving on the Denver side and 12 hr 5 min on the New Orleans 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 Denver and New Orleans 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 Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and New Orleans.
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 →
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 →
New Orleans is a consolidated city-parish located along the Mississippi River in the U.S. state of Louisiana. 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.