Unchurched people think of church as boring, irrelevant, and predictable. You need to avoid these perceptions at all costs.
What is a felt need you can focus on that people will find interesting? Is it controlling finances? Building a strong family? How about tackling the issue of peer pressure and what the Bible has to say.
Have free activities other than VBS for families to take advantage of. VBS tends to attract the kids of your church as well as other churched-kids that attend. Use your own congregation to invite families without a church home and support your initiative with digital campaigns in Facebook and Google Display Network to send out invitations.
Maybe it’s a BBQ and water slides. Or perhaps a free date night for the parents while you watch the kids with a movie and pizza. Or what about a community activity that kids can be a part of? The options are endless but you need to promote!