Final answer:
A total lunar eclipse at midnight at your location would also be visible to another person 200 miles away, provided they are on the night side of Earth and it's clear. Visibility of a lunar eclipse does not vary much over this distance.
Step-by-step explanation:
If there is a total lunar eclipse at your location at midnight, another person 200 miles away from you would see the same lunar eclipse provided they are on the night side of the Earth and have clear skies. Unlike a solar eclipse, which is visible only from specific locations on Earth, a lunar eclipse can be seen anywhere on Earth's night side because Earth's dark shadow is large enough to cover the Moon several times over.
The visibility of a lunar eclipse does not change dramatically over a distance of 200 miles, so both you and the other person would experience the eclipse simultaneously. Factors such as weather and local topography might affect individual viewing experiences, but generally, both observers would witness the Moon being obscured by Earth's shadow at the same time.