How far did the Star Trek crew went with their warp speed ships. Did they went 8 billion light years away or were they Lurking in this milky way Galaxy!
In general, Star Trek stayed relatively close to Earth due to most peer star systems within a few thousand light years and therefore reachable within days or weeks at TOS era warp speeds (which generally topped out around 100c). In the TOS episode "By Any Other Name" the Enterprise was taken over by the Kelvans who modified the ship to make the journey back to the Andromeda Galaxy within 300 years. However, the ship only left the Milky Way for a short period before Kirk and Company regained control and headed back (the same happened in the TOS episode "Is There in Truth No Beauty?")
The Enterprise also travelled to the "center" of the Milky Way in Star Trek V, but this clearly was nowhere near Sagittarius A*.
As noted above, in the TNG episode "Where No One Has Gone Before", thanks to The Traveler the Enterprise-D travelled pas the Triangulum Galaxy (M33) which is 2.7 million light years away.
And, of course, Deep Space 9 and Voyager both took place on opposite corners of the Milky Way from where Earth and the other worlds of the Federation reside.