Your innkeeper was evidently saying βίωσε βίο, his modern Greek for "live life." In ancient Greek, however, βίος had a more specialized meaning, something like "life style" or "manner of living." In Plato, for example, βίον βιοῦν means "live life" in the sense of living a particular sort of life, or living in a certain manner or fashion.
By contrast, your "live life!" seems to relate more to the act of living itself, to being "lively," rather than to content or style of life. For that, ancient Greek would need the more "biological" verb that I gave you as an imperative, ζῆθι. And it has the added spice that it's spelled with the ancient numbers for the hours when you could really get out and "live."