In Acts 2 and 1 Cor. 14:23 we see non-believers attracted and challenged by worship.  We learn there that non-believers are expected in worship, and that non-believers must find worship challenging and comprehensible.  In city-centers where there are a mixture of world-views, it is crucial to include both Christians and non-Christians in the same service -- even in many of the other meetings and ministries of the church....  Why?  In a "mixed" group, when the preacher speaks somewhat more to non-Christians, the Christians present learn how to share the faith....  On the other hand, when the preacher speaks more to Christians, the non-Christians present come to see how Christianity "works"....  In short, a center-city church should not simply "do mission" or "do evangelism."  Every part of its ministry should be geared routinely both to Christians and non-Christians, and expecting non-Christians to be "overhearing" whatever is said and done in any context.

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If you speak and discourse as if your whole neighborhood is present eventually more and more of your neighborhood will find their way in or be invited.  Why?  Most Christians, even when they are very edified in church, know intuitively that their non-Christian friends would not appreciate the service.  What you want is for a Christian to come to your church and say, "Oh!  I wish my non-Christian friend could see (or hear) this!"  If this is forgotten, soon even a growing church will be filled with Christians who commute in from various towns and communities far and wide rather than filling up with Christians and seekers from your church's immediate neighborhoods.