[atoav]

By now I think they managed to measure relativistic effects of clocks that are a few milimeters apart in terms of distance from earths gravitational center.

[pvg]

Sufficiently clever experimentalists also pulled this off in about 20 meters in 1959, the clever bit being ditching the clocks entirely:

https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment