Although the light year is a commonly used unit, astronomers prefer a different unit called the parsec (pc). A parsec, equal to 3.26 light years, is defined as the distance at which 1 Astronomical Unit subtends an angle of 1 second of arc (1/3600 of a degree) When we use the parsec for really large distances, we often put a prefix in front of it - like kiloparsecs (kpc), which are equal to 1000 parsecs - or Megaparsecs (Mpc), equal to a million parsecs.
The Milky Way is about 1,000,000,000,000,000,000 km (about 100,000 light years or about 30 kpc) across. The Sun does not lie near the center of our Galaxy. It lies about 8 kpc from the center on what is known as the Sagittarius arm of the Milky Way.