Quasars in brief are extremely active galactic nucleus surrounded by dust, gas and stars. Quasars are located billions of light years away from our galaxy. Most were formed not long after the creation of the universe, 13.8 billion years ago.
Our Milky Way galaxy is inactive at the moment, its not to say that our galaxy was never a Quasar in its early life nor could it become a quasar again. It is theorized that when the Andromeda Galaxy collides with our galaxy, the supermassive black hole at the centre could become active again due to having consumed a lot of materials. This might be scary but you need to realise that this won't happen for billions of years. The Andromeda Galaxy is only moving at about 75 miles a second towards us and its a long way away. Universe Today
The furthest quasar at the time of writing, February 2018 is ULAS J1342+0928, it is in the constellation of Bootes, the Bear Driver or Herdsman. The Quasar is about 29.36 Billion Light Years away and what we are seeing now is what it looked like a mere 690 million years after the The Big Bang when the Universe was formed. If we were to travel to quasar now, it will probably be inactive and be a regular galaxy like our own having finished feasting.
The previous record holder of furthest quasar was ULAS J1120+0641, a quasar that is located in Leo constellation. It was discovered in 2011 and therefore held the title for nearly seven years. The quasar is about 28.85 million light years away and we are observing it as it looked 770 million years after the big bang. Wiki
The numbers in the names are the RA and Dec locations of the coordinates. ULAS stands for UKIDSS Large Area Survey with UKIDSS standing for UKIRT Infrared Deep Sky Survey. UKIRT in turn stands for United Kingdom Infra-red Telescope which is situated on Mauna Kea dormant volcano in Hawaii.
The quasar has a mass that 800 times the mass of our own star, the Sun. The location of the Quasar is R.A. 13h 42m 08.10 and Declination +09d 28' 38.61. The estimated location of the quasar is shown below. It is too faint to see the quasar with the naked eye.