D., I had this same concern when my daughter and I relocated to Illinois. And let's face it, if you are anything like me and would prefer to do the shopping and oil change without worrying about your kids getting restless while maintaining your sanity; baby sitting can be expensive.
I actually couldn't find any teenagers because the referrals were highly involved in after school activities. So I started networking with other single or SAHM's and began trading baby sitting services, which has worked out perfectly. One single mother that my daughter likes loves to go out in the city so I will watch her son over night so she is free to go out and we don't have to worry about her waking us up to pick him up. We can call each other for any need, hair and medical appointments, etc.
And when I need to go shopping, my daughter is excited to go play at her house. If you don't know any other mothers (married or divorced/single), try joining a professional women's group near you at meetup.com to start building relationships with another mother/family, you and your kids will trust and can exchange playdates for FREE. This avenue will allow you to arrange fun activities for them at no cost to you and the kids are having fun.