Speed of light is a problem in that it makes a lot journeys essentially one-way.
If we're talking about manned-space travel, the acceleration needed to get to anything approaching the speed of light would itself take months, if not an entire year.
So that's two years of travel just accelerating and braking. And to the next nearest star, you will probably be traveling at speed for somewhere around 3 years. I'm just assuming that you'd travel half a light year accelerating and braking. It's likely wrong. But I also suspect it's generous.
That's 10 years round trip to get to our closest neighbor.
And yes, while time dilation would cause those on the vessel to experience far less time than that, the people on Earth will still experience every minute of those ten years. It's also about 9 years before you even get a message. Because at least the information can be sent at SOL without having to worry about killing the messenger. 5 years to get there, 4 years to send a message back.
And some people will say "well, what about Von Neumann probes". Well, that still has the problem of at least a decade long wait to see if you have any return on that investment. And it assumes that we can develop artificial intelligence to the degree that such probes are possible. Which is a big leap considering we don't even really know what intelligence or conscience even is. We know what it can do, but we don't know how either works.
So, in order to colonize the galaxy, a civilization needs to be able to dedicate enormous resources to projects where the potential payoff, if any, are going to be at least a decade away. And to have developed technology far surpassing anything we have at the current moment. To have figured out very fundamental questions about exactly what life is.
Yeah. I'm not surprised we haven't seen any extraterrestrial life. The universe is simply too vast.