If these spaceships are going faster than the speed of light, then presumably they're moving faster than it would take them to see upcoming stars.
So how come they never run into one?
Warp speed is supposed to be like ftl right?
Light emitted from the stars in times past does NOT have to catch up with the ship. The photons are already there, traveling between the stars.
STL or FTL, the ship will have no problems seeing them.
But you do have to take into account a star's own motion through the galaxy, in accordance with its proper motion and radial velocity as viewed from Earth.
As you approach a star, you will be seeing it with light that was emitted from it at later and later times along its own trajectory. From your perspective, its position in space will therefore appear to shift as you approach it. Your journey to the star will have to take that into account so that you arrive where the star actually is, instead of where it was.
If you have no FTL sensors, an accurate assessment of the motion of the star is therefore essential. Hypothetical instantaneous FTL sensors would mitigate the problem of unknown factors, by locating the star where it actually is, so to speak, so that you can head directly there (as a good approximation for short travel times; or refined with proper/radial motion for a higher-order correction), which is generally speaking not where the light shows it to be.