Both Star Trek and Star Wars pretty explicitly limit themselves to a single galaxy.

Star Trek occasionally comments on other galaxies as being very far away; for example, Kirk once noted that it would take thousands of years to get to the Andromeda Galaxy. Also, Voyager was transported to the "Gamma Quadrant", which is a quarter of the Milky Way disc, and it was impossibly far away from the "Alpha Quadrant" that the vast majority of the rest of Star Trek occurs in. The stable wormhole near to Deep Space 9 and Bajor led to and from the "Delta Quadrant", which had been unexplored territory before the discovery of the wormhole. Also, the original series shows there being a nearly impenetrable border at the edge of the galaxy.

Star Wars is less explicit, but it does state that it happens "in a galaxy far, far away".

Normal Star Trek speeds max out around 1500c, though, which still means that it would take decades (5-ish) to go from one end of a quadrant to the other.

I'm not familiar with Star Wars speeds.