Two words in St Luke’s Greek vocabulary are ‘kataluma’, where the Last Supper took place and which is usually translated ‘upper room’ (22:11, see also Mark 14.14), and ‘pandocheion’, where the Good Samaritan took the injured traveller and which is usually translated ‘inn’ (10:34). So in 2:7, describing the birth of Jesus, when he writes ‘there was no room in the ____’, which word does he use? ‘kataluma’, the upper room or guest chamber of a private house.
The Bible Gateway website compares 51 different translations. 34 of them (just on two-thirds) use ‘inn’. Other translations are: village inn 1, ‘inn [or guest room (of a private residence); or caravan shelter]’ 1 (the Expanded Bible), guest room 4, guestroom 1, guest-chamber 1, guest quarters 1, chamber 1, hostel 1, the house for strangers 1 (which suggests more a commercial inn than a private house), living-quarters 1, lodging 1, lodging place 1, the place where people stay for the night 1, malon (inn) 1 (the Orthodox Jewish Bible; ‘malon’ appears to be the Hebrew word for ‘inn’). There are several other Greek words translated ‘lodging’.
For what it’s worth, I am quietly convinced that Jesus was born (or at least slept the night (there is nothing in Luke’s account which is inconsistent with Mary giving birth somewhere else, slightly more comfortable, in the inn or house)) in the ‘garage’ of a private house.
Does this matter? Theologically, no – ‘the Word became flesh and dwelt among us’. In terms of the iconography of Christ-mass cards, probably.)
A happy and holy Christ-mass to you.
(ha! I first typed ‘Geek’ instead of ‘Greek’ in the first sentence.)
(PS I cheerfully admit that I have never actually studied Koine Greek or theology, just eclectically read a bit about the former and a medium to lot about the latter along the way, so I might be wrong about a lot of things here.)