J.
Welcome to Oak Park! It's really a wonderful community. But it is hard to find a center spot in or near Oak Park for a younger child. That's how we ended up using licensed home daycare. Some of the home daycares are closer to centers in size/staffing/enrichment options, and some are more like homes. The West Suburban Home Daycare Association can give you referrals if you're interested (they used to have a website, but all I can find offhand is this: ____@____.com or call ###-###-####.) Or email me if you aren't able to reach them and I can pull together some information for you on daycares that I know of.
There's also a daycare and schools referral guide for the area. Of course I can't find mine now that I'm looking for it, but I think the visitor's bureau might have some.