It seems that film and book might have different interpretations of this.
I really don't remember book that well, so what do we know about the film interpretation related to offworld travel and distances.
1) Travel between Earth and at least one colony takes comparatively little time (all quotes are from the BR script):
Bryant: There was an escape from the off-world colonies two weeks ago. Six replicants, three male, three female. They slaughtered twenty-three people and jumped a shuttle. An aerial patrol spotted the ship off the coast. No crew, no sight of them. Three nights ago they tried to break into Tyrell Corporation.
So, at most the travel from colony to Earth took 11 days; more likely less, since we would presume replicants had to take some time to orient themselves.
If we are talking sub-light speeds of anything compared to our current capabilities, this is out for even the planet that is closest to Earth at some time: Venus -- Universe Today lists the fastest journey so far to have taken 110 days.
So, we are talking either at least 10x+ faster sub-light speeds than currently possible, or generation ships or some sort of hyperjumps.
2) Replicants (at least the Nexus 6 model) have a 4 year life span:
Bryant: The designers reckoned that after a few years they might develop their own emotional responses. You know, hate, love, fear, anger, envy. So they built in a fail-safe device.
Deckard: Which is what?
Bryant: Four year life span.
This one means that generation ships are out, unless we're talking cryogenic freezing or something similar, or replicants would not arrive at colonies at all.
Also, you don't need a generation ship for a travel of 11 days after all.
3) Tannhäuser Gate
This part is subject to quite some interpretation, however, there are some things which seem logical to me.
As noted in one of the previous answers, Roy Batty's "Tears in the rain" monologue includes references to events he himself witnessed apparently near Orion. Orion nebula is approximately 1,344 light years distance from Earth. Alternatively, he could be talking about Orion constellation, which would also make sense, as Orion is a hunter in Greek mythology and therefore his constellation would naturally have a "shoulder". It doesn't change the underlying idea, however, since even the closest star in the Orion constellation is more than 200 light years away.
If we accept Roy's monologue that way, it means that during his near 4 years of life he has managed to get somewhere near Orion nebula/constellation. It is possible that he was posted there and later on got back near to Earth, however, at any rate the implication would be that there is some sort of FTL travel in BR universe, at least in the film version.
As I mentioned in a comment, I have always assumed that the Tannhäuser Gate mentioned by Roy in the same monologue is some sort of warp gate or similar. This view is apparently shared by other viewers up to the point that it is mentioned in BR fandom wiki entry.
As a coherent alternative, if we assume Roy was speaking of seeing attack ships that appeared to be "off the shoulder of Orion", but in fact were there only in that direction, but not distance, then we could assume that off-world colonies are (at closest), for example, just Mars and/or Venus (assuming you can see Orion nebula well enough from there), and the 11day travel is simply ~10-20x faster rockets.
This would tie in better with the book, which speaks of colony on Mars etc, as written in another answer. And we presume script writers read the book after all. In that case you could argue that book talks about sub-light travel speeds in all cases. The journey to Proxima Centauri, which is mentioned in the book as described in @Nicola Talbot's answer and which @anaximander calculated as done at around 0.1-0.2c would fit as well, leaving slower speeds for inner system travels (probably because of not enough space/time for acceleration to 0.1c between Earth and Solar system planets)