A great way to connect with the kids of your community is to open up your church during the week outside of regular church times. For example, if your church is blessed with a gymnasium, place a banner out front advertising an open gym one afternoon a week/month for a couple of hours. Allow kids to come in and play (with supervision) and offer a light snack. This provides a chance for kids to build a relationship with you and get exposed to your church.
Another option is to offer free tutoring once a week. Many children need assistance with their schoolwork but cannot afford the cost for extra help. Do you have people in your church who could donate an hour or two each week/month to help children?
Another opportunity for your church to connect with kids and parents from your community is to offer a Parents Night Out. Once a month, give parents a much needed break by offering low cost or free childcare. You may decide to offer this as a free service or charge a small fee to cover the cost of snacks/food/activities/etc. Pre-registration should be required in order to insure the proper number of volunteers needed. You are ministering to children through a fun time of play, activities, and learning about God while also meeting a need for parents.