For my daughter's 2nd we invited some friends to join us at a lovely gelato place in Evanston called Linz & Vail. They have 2 locations and there are parks across the street from both (though I prefer the location on Noyes). The idea was get gelato then go across the street to play. It rained for our "party" but all the kids just mingled about the shop. They have a TV and toys to play with in a little room on the side. Plus their gelato is heavenly! http://centerstagechicago.com/restaurants/linz-vail.html
There's also the Choo Choo Diner in Des Plaines. It's a 50's style diner that serves your food from a train track. It is small and gets crowded and is only open at weird times. But if your girls like trains it could be fun. http://www.thechoochoo.com/
We're also HUGE fans of Lamb's Farm in Libertyville. I spent the day there with my son when he was 2 and we had a ball! They have a train to ride, animals to pet and look at, a park, an ice cream stand, a pet store, merry go round. You can easily find lots of fun and it is VERY kid friendly and stroller friendly as well. http://www.lambsfarm.org/
Have a great day whatever you do and congrats!