Où vous allez ? À l'auberge la plus proche, à vue de nez.
I’m torn between two interpretations:
Where are you going? To the nearest inn, I guess.
/ Suggesting that this is just a wild guess. /
Where are you going? To the nearest inn, approximately?
/ Practically, it is hard to say for sure which inn is the nearest, but indicating the one apparently nearest, roughly speaking. /