distances - How many light years away is Earth from the closest outer edge of the black hole at the center of the Milky Way?

As @Py-ser already said, there is the very clear information about that, although his link correctly is here.

As we can read there, the distance of this is around 25000 light years, with a precision of 1400 light years.

Normally, the size of most galaxies is around some ten thousands of light years. Compared to the black holes, their size (the diameter of their event horizon) is some kilometers (stellar black holes) or some astronomical units (some millions - hundred millions of kilometers).

Even the size of the event horizon of the greatest known black hole is around the size of the solar system, which is around some thousandth of light years.

You don't need to ask, "how far we are from the nearest edge of Sagittarius A*", you can simply ask "how far we are from Sagittarius A".