S.V.
The Schaumburg Park District actually has a class called Just for Me, but kids have to be at least 28 months old. It's 15 minutes together, 45 minutes just kids and teachers, then 15 minutes togther for a book and snack. My daughter's been going with Grandma and seems to like it.
Prince of Peace Lutheran Church on Higgins also has a Parent's Day Out with their preschool but it's 3+.