Generally speaking, you can take something like a dozen quests before you are stopped, quests only help to give you that compass marker, and you can kill something and report it just like a quest would, so there's no particular need to even be on a quest in the first place, so worrying too much about it is pointless. Just do whatever you feel like and occasionally tell people you just killed something worth bragging about.
With that out of the way, it depends on what sort of location you are in, and what sort of creature you are looking for.
In general, that compass points to the middle of the worldmap tile that has that creature in it, not the creature itself. This is important in cities, because it basically only points to the center of the city instead of the creature. Basically, don't bother looking for them in cities. Explore cities for fun and maybe kill some bandit leaders, but don't expect to find everything. The game's procedural sewer generation will create sewers that are impossible to reach without the ability to mine.
If you are looking for a werecritter, however, what you are looking for is almost always a single down ramp that leads to a lair. It will be somewhere in the 48x48 tile box in the local area that you can travel through, and it's really hard to see sometimes if you are using some tilesets like the standard one.
Alternately, a lair can sometimes be a small crevice in a slope instead of just a down ramp. Check to make sure there are actual walls in the whole area, and you didn't just walk right over a cave entrance and didn't notice because you didn't check on that z-level.