Hi T., and welcome. I live in Oak Park. Do you want full day/daycare or partial day preschool?
Oak Park district 97 has a free, half-day prek program at Longfellow school during the school year. Families need to have a qualifying condition, but you would probably qualify because of your move (other examples that have qualified kids I know for the program include things like new sibling, bilingual).
The area has lots of montessori schools, and I know people who have had kids in most of them (Alcuin, Intercultural, Keystone, West Suburban, Oak Park Montessori, Morningside Academy, Children's Garden) most of them provide both half-day and some kind of full-day option. Pilgrim is a half-day, 4 day a week program so if you need fulltime care that might not work for you. Concordia University in River Forest has an excellent preschool program but a long waiting list. There are others . . . email me with what you have in mind and I can make more specific suggestions.
The visitors center should have a copy of the Guide to Early Childhood, which is an extensive listing of options. TheAlso, the Wednesday Journal has their Answer Book on newstands now and in the visitor's center - that will also be handy for a new resident.
Good luck!