In the case that traveling faster than light or using 'shortcuts' via wormholes isn't possible, the conclusion must be that whoever is out there and whatever kind of technology they may possess, they'll be 'grounded' in their own galaxy unless they are up for spending millions of years traveling to even their nearest neighbor.
The Milky Way's nearest big neighbor, M31 - The Andromeda Galaxy, is 2.6 million Light Years away from us. Meaning that even if one could travel at the Speed of Light, one would have to be on the move for 2.6 million years - and that's just the nearest big neighbor. (There are some smaller galaxies closer than Andromeda but Andromeda is a good reference point and people know about it. In either case it's practically 'next door' in relative terms.)
Being able to do this however means having reached an extremely advanced level of technology - we're talking 300,000 KM/Sec or 1,080,000,000 KM/Hour. So let's ask ourselves how likely it is that there's even ONE of those civilizations for every galaxy out there. Well, who knows. There might be 100 per galaxy or there might be 1 per 100 galaxies. Or none at all. What's likely or not isn't the topic however - the goal is to paint a picture of how it really is if FTL (Faster Than Light) is impossible and 'shortcuts' through time and space just isn't happening for any civilization, no matter how technologically advanced they are.
One could talk about cryonic hibernation (the freezing of a body to suspend it) for long travels but we're still talking such vast distances that even if a civilization out there did endeavour on such a massive project (to travel millions of Light Years - just to reach their nearest neighbor), they'd still be unable to go very far in relative terms. As in they wouldn't be able to cover say even 0.1% of the total distance between peripherals (if there even are any peripherals - the 'edge' isn't really where we see it but much further out!) in the vast expanse known as the Universe.
So.. somewhere out there there might be this hyper-advanced civilization who have overcome all the hurdles (surviving all the things that could go wrong over a long period of time basically) of reaching such a point that they are at the very technological limitation (or the intergalactic speed limit, which would be the Speed of Light, if you will. And remember, no 'shortucts' either)..
.. yet in reality they have to be content with only having the opportunity to explore their own galaxy. Let's say they live in a galaxy the size of the Milky Way. 250,000,000,000 stars (some say this number might be 4x higher but that's another story). The Milky Way is roughly 100,000 Light Years in diameter. Traveling from one end of their galaxy to the other would thus require them to be on the move for 100,000 years. Or in case they were only really interested in their local star cluster within their galaxy, they'd still have to travel up to 5,000 years to cover enough ground to even be able to plot out a small circle on their map of their galaxy and say they've explored this part. All this at a speed of over 1 billion KM/hour, the Speed of Light, mind you.
Estimates are that there are at least 100 billion galaxies in the universe, but this number is probably much higher. Most scientists would probably give you the number 200 billion if asked but if you inquired more thoroughly with those sames scientists, they'd easily give you numbers such as 500 billion or even 1,000 billion, it's just hard to say.
The reason for this is that wherever you are in the universe, you are in the center of the universe. Picture a circle around your location and that is the entire universe. The edges of the circle is 13.7 billion Light Years away. Now let's say someone 5 billlion Light Years away from you does the exact same thing. He too would be at the center of the universe and the edges of his circle would also be 13.7 billion Light Years away and those two circles would overlap each other. This is because the edge is as far away as the light has traveled since the supposed beginning of time and we can not see any further. But meanwhile, the universe have expanded and the edges are actually much further out - and there are galaxies there too that we can't see.
If you ever laid down on a football field and looked around, you'd see a lot of grass. Some person figured out that there are about half a billion straws of grass on an average football field - multiply by 1,000 and you have 500 billion. One straw of grass for every galaxy out there. Ish.