Don't wait for them to come over. Ask if there's a neighborhood phone directory and find out where you can get one. Ask for recommendations on babysitters. Ask how their children like the sitters. This will lead to many a good relationship.
Most families are very willing to help.
If you stick to those that are only in your area of most interest, you could be missing out on some wonderful relationships. Contact the local Welcome Wagon. There's one in almost every town. Many churches now offer parenting and play groups that are embraced by the whole community, not just members. Go for a family walk.