You can expect GREAT beauty; A sense of peace, of awe, of thankfulness, of community, of continuity.....I originally hail from that neck of the woods and would suggest late September or early October; strictly for the beauty of the area and the weather, and if that is too soon, I would hold off til mid spring at least, for the same reasons. You really don't want to be there in the winter or the heat of the summer.
Autumn is probably still very nice, but definitely do not go to Chicago during the winter!!!
The Wilmette temple is awesome! Give yourself extra days to soak it in, walk the gardens, and pray.