Once you're outside, fast travel (teleport) to the location of where you got the quest by clicking on the area in your map.
The only real walking in the game is exploring new locations (part of what makes the series) and you can always buy a horse to go faster.
Whoa whoa whoa, didn't know about the fast travel back thing. Don't get me wrong, I love exploring new areas, and when not running 'back' the same way, it's a great game. For example, I went to that cave to find the horn, which was already stolen, now I have to run all the way back home, the same way I came, so i'll see if the teleport works for that, if so, the game just became much better.