Essentially you need to have a block party. This is after all an outreach ministry or at least it should be for each church. The goal of VBS is to bring children and possibly the parents as well to Christ.
So with outreach as your goal you need to make your end of VBS party a family event. Highly encourage your VBS participants to bring their families. Have your even immediately after VBS on the last day.
Serve food and refreshments. Hotdogs, chips and cookies are a good start. Make sure you stress it is FREE.
Remember I said block party? Yes you need to have a bounce house or something big and exciting that kids will want to stay making it harder for parents to say no to staying around. Have some other games like bean bag tosses and maybe a Photobooth.
Whatever you do make sure you make it a family event. Have a craft table and make sure to play some music perhaps having the VBS sound track on repeat.