http://news.bbc.co.uk/2/hi/science/nature/7774287.stm
"The black hole is four million times more massive than our Sun, according to the paper in The Astrophysical Journal...The researchers from the Max Planck Institute for Extraterrestrial Physics in Germany said the black hole was 27,000 light years, or 158 thousand, million, million miles from the Earth. "
Also today's APOD:
http://antwrp.gsfc.nasa.gov/apod/
"Astronomers patiently measured the positions of the stars over time, following one star, designated S2, through a complete orbit as it came within about 1
light-day of the center of the Milky Way"
1 light-day from a black hole sounds pretty close.