Kim -- it's often easiest for families to meet other families through school. Beyond your daughter making friends at her school, you may want to see if you can volunteer at her school (time permitting, of course).
There are also lots of extracurricular/enrichment activities in the area, from classes at Hamlin Park to art/music classes in Roscoe Village to sports activities. Does she like to play soccer? AYSO. Art or music? She can try August House or Old Town School of Folk Music.
You may also want to look into volunteer activities such as helping out at a food pantry or animal shelter.
Yes. You make friends through common interests. Our truest friends are those with many layers of similar interests and same values. And mostly when parents are friends too. :) get involved together in stuff. Church is a big one :)