Please check out this great article on biblical hospitality by Matt Chandler (a pastor in the Dallas area). This is one area that our church is trying to work on right now — being more outward focused, inviting our neighbors and colleagues (particularly non-Christian ones) into our homes and lives — not to mention the more primary task of inviting one another into our homes and lives, beyond seeing each other once a week on Sunday mornings. 

Here are some choice quotes from the whole article.

The ultimate basis for hospitality is theological: 

why would the Bible be so serious about hospitality? ... It’s because God has been hospitable to us. Even when we were living as his enemies, God came and saved us. He opened the door and invited us into his presence. We demonstrate that we truly appreciate the divine hospitality we have received as we extend our own hospitality to those around us.

On why (effective) evangelism and hospitality go well together in our culture:

But might it not be, in our cynical, polarizing, critical, dumpster-fire culture, that a warm dose of welcoming hospitality will take some folks by surprise and open up the door for opportunities to make disciples of Jesus Christ?

Four tips on how to be more hospitable: 

1. Welcome everyone you meet (that is, greet everyone)

2. Engage people (ask sincere, open-ended questions of everyone)

3. Make dinner a priority

4. Love the outsider ("we love the outsider because we were the outsider")

On the need for courageous hospitality: 

These sorts of things actually require courage, because they force us to rely on the Lord and his strength—and not our own. When we open up our homes and build friendships with those who don’t look like us, believe like us, or act like us, we open up our lives and make ourselves vulnerable.