The Christmas associations of an inn and an innkeeper, however, do not reflect the language of Luke’s text in 2:7. Rather, the word usually translated as “inn,” seems to refer to either some type of reception room in a private home or some type of public shelter. Since this place was full, refuge was sought elsewhere. The animal room that Joseph and Mary found may have been either a stable next to the place of lodging or a cave, since use of caves for stables was common. Ancient tradition associates Jesus’ birth with a cave.
–Paraphrased from Darrell Bock, Luke 1:1-9:50, BECNT pg. 208.