When I moved to this Chicago suburb, I quickly got to know people when I joined a church and volunteered to help out in their church nursery. That way I got to meet other young women/moms and ended up a few years later as president of their small church nursery club. You could also teach Sunday School (the lessons are all laid out with good teacher manuals) or just sit in on some Bible classes, even as a non-member of the church (and check 'em out!).