Undersea by rail. Ninety minutes from New York to Paris: 5600 km
[1] https://www.physicscentral.com/explore/poster-earth.cfm
This approximation accounts for this fact: "As you fall there is less and less mass between you and the center so there is less and less to pull you down"
This approximation accounts for non-uniform density of the earth:
> Klotz based his calculations on the internal structure of the planet as determined from seismic data. While the Earth's crust has a density less than about 187 lbs. per cubic foot (3 grams per cubic centimeter), Earth's center has a density of about 811 lbs. per cubic foot (13 grams per cubic centimeter). The density of the planet does not rise in a straightforward manner the farther down one goes — there is a sharp 50 percent increase in density at the boundary of the planet's mantle and its outer core about 1,800 miles (2,900 km) below Earth's surface.
> Now, using a more realistic model of the Earth, Klotz finds the fall would take only about 38 minutes and 11 seconds, about 4 minutes faster than thought.
The future is bright: wheels in space, underwater trains, and everyone gets a spandex jacket.