Does someone need to invite people into their homes to practice hospitality? I know this is not the only way to serve.
The word "hospitality" can translate the Greek word philoxenia. It is a compound word of "love" (philo) and "guest room or lodging" (xenia). This word is used in Romans 12:13 and Hebrews 13:2 and refers to the enjoyment of having people stay with you.
The word "hospitality" can also translate a related Greek word philoxenos. This is a compound word of "love" (philo) and "stranger or guest" (xenos). This word is used in I Timothy 3:2; Titus 1:8; and I Peter 4:9.
Hospitality is about sharing the things that I have with others -- my home, my food, my time, etc. It is about getting to know people on a personal level. Putting someone up in a hotel and buying them breakfast has as little to do with hospitality as sending money to an orphan's home has to do with visiting orphans (James 1:27).
When I think of hospitality, I am reminded of a family up in Anchorage whom I recently met. Knowing that we were up there to see our son, they ask if they might be able to intrude and have us all over for dinner one night. We had a wonderful time and a wonderful meal and as we were leaving they were profuse in thanking us for taking the time to come to their house -- it was hard to get a word in to say that we were honored that they asked us in. That is a love of strangers! We left knowing we made the acquaintance of new friends.