If you are willing to travel to Deerfield, I highly recommend Deerfield Community Nursery School. (There is a family in my daughter's class who travel from Lincolnshire.) They have a Mom and Tot class for children at least 18 months old, and for children who are 2 by May 1 they can be in a class called All by Myself which is without a parent. We started my daughter there when we moved to the area 2 years ago from out of state, and it has been wonderful for her and me too! The teachers are fantastic and very skilled in helping children who might have a hard time with separation anxiety. They have one of the smallest child to teacher ratio in the area. My daughter has learned so much not just academically but also socially and has gained much independence and confidence. I can't say enough about the program they have for children.
In addition, if you would like to get to know the other parents (mostly Moms who stay at home), there are social events which you can take part in. The moms have a once a month social night out. Also it is a parent-run Board of Directors, so there are plenty of opportunities to get involved if you would like to be part of shaping the school. The other families are extremely friendly, and some of my closest friends here are other moms from her school.
Feel free to contact me if you would like to talk more...