What instrument measures mileage?

Answer 1

An odometer is the most typical mile measuring device. A topofile plays out a string against a wheel which can also measure miles. More cumbersome yet one could use a chain or tape measure. Less cumbersome would be a laser. Even small survey lasers can accurately measure a mile.

You could time sound waves using a clock, or light reflection with an extremely accurate clock.

Given a known "height" standard, you can use parallax (surveyor's theodolite).

For light years, you can use "standard candles"... stars of known mass / intensity, and measure the intensity of the unknown distant object. The instrument for this would be a photon counter.

For objects outside the Virgo supercluster, you can use redshift of characteristic wavelengths--measured by a spectrophotometer.
well if I had to say it would be a odometer or a trundle wheel

Answer 2

In a car it is called an odometer.
An 'Odometer' measures mileage.