A.S.
There is a gym class and a mom/tot tumbling class through the LaGrange YMCA (Kemman and 31st - LaGrange Park) that meet actually at the MAX. There is also a busy baby yoga class (mom and child) at Focus Yoga studio in Brookfield. There is Dance Center of LaGrange that has pre-ballet on tuesdays for children 2.5 - 3.5 years. I think that one is actually without parent, from waht my friend told me. There is soccer at Chicago Sports Zone in Melrose Park for kids 18 mos and up.
These are just some of the under 3 activities I've found (my daughter will be 3 in Nov, so it's been a challenge finding classes for her age this fall).
As far as playgroups, I'm goign to look through my past posts on here because I asked the same question and there are a few in LaGrange, but I can't remember where htey were (we ended up meeting a lot of people through the YMCA and never went).
Another option is to check out your local and the surrounding park districts for classes. I know LaGrange Park, LaGrange and Brookfield all have good offerings. Brookfield is limited, though people have said nice things about hte classes. LaGrange has a lot of classes and activities and outings.