A.R.
Someone already posted my suggestions, so just wanted to give lots of thumbs up to:
1) Marshas Music Together
2) Hyde Park Parent Support Network (PSN)
PSN has informal playgroups (join anytime, free), a playroom, and a listserv, which I used to create a playgroup for my son 4 years ago. Fabulous resource, about 250 members in Hyde Park.
Forgive me if I'm repeating, don't recall if these were mentioned:
* Hyde Park Neighborhood Club (55th and Kimbark, various activities for all ages plus tot lot -- open playroom, inexpensive.
* Chicago Park District was mentioned, just wanted to say my children have really enjoyed gymnastics (at that age, they program is low key skills development and a lot of fun) -- they use Chicago State University facilities on 95th and Cottage Grove. I applied through Chicago State.
* Family Resource Center (if you're affiliated w/ U of C)
I hope you have a safe and easy move!