Then I like to say the nearest next start is roughly 4 light years away. So even at 17km per second, or about 10.5 miles per second, it will still take approx 72,000 years for it to reach the nearest star.
That star is 4 light years away and our galaxy is about 100,000 light years across. The next galaxy is about 2.5 million light years away!!! So at the incredible speeds of one of our fastest man made objects it would take something like 45 billion years to just get to the next galaxy!
Seeing how the known universe is estimated at over 46 billion light years in size and looking back on the other numbers I wrote it quickly becomes apparent that to travel across the galaxies one would need to be able to reach unbelievably unimaginable speeds. Even the speed of light as you mention would not be even close to fast enough to get anywhere significant.
On a side tangent I was always a trekie back in the day. I know their warp drive was faster then light but now I almost want to go back and look at the math of how fast they must have been going to be going the distances they were going.
While there's a rough polynomial (v =~ c * w^3, I think) for post-TOS Star Trek warp factors, the only consistent rule: a starship travels at a velocity that helps tell a good story.
It's fun to try mapping Star Trek stories, anyway; it helps you ponder how much time they must have spent in transit. They have to find things to occupy their time.
But I absolutely loved the show growing up so not here to knock them. I am sure in hindsight they may have come up with a better definition of how warp speed works and how they can travel great distances. I won't think about it too much.