The galactic GPS would be based quasars, e.g. far away galaxies, that would pretty much appear the same positions anywhere in the Milky Way. Quasar spins are gradually slowing down. So you could tell how many light years you are from the quasar by the observed spin rates. In addition, you can determine epoch time from knowing position a spin decay rates.

Carl Sagan put a quasar GPS on a golden plaque on both Voyager probes, so future intelligences could tell where and when the Voyagers came from.