I just threw a birthday party for my 3 year old twins. We made the food ourselves, but it strikes me that with the 1-3 year old set, especially for "snacks", all you'll need is some fruit (think non-staining - apple slices sprizted with lemon to prevent browning, green grapes, raisins, maybe pineapple) and a giant carton of Pepperidge Farm Goldfish. Add small water bottles and some real juice boxes and you are set. Parents will love the healthy choices.
For the adult snacks, I love
Panozzo's. It is not exactly in Lincoln Park, and you'll have to go pick it up, but they will be happy to customize the order. You could get a tray of pasta or Caprese salad, and some sandwiches cut into small slices, and the parents would enjoy them, as well as the bigger kids.
Finally, for desert you probably already know of
Sweet Mandy B's. The kids and parents always love their cakes and cupcakes.
Good luck!
Today I caught that fish again, that lovely silver prince of fishes,
And once again he offered me, if I would only set him free—
Any one of a number of wonderful wishes... He was delicious! - Shel Silverstein