I grew up in Evanston, which is the first suburb north of Chicago on the lake. It is a beautiful town, and given good weather, I would recommend a nice, leisurely walk around, and especially along near or along the lake, including the Northwestern University campus. Evanston can be reached easily by the "L" (i.e. elevated) train from almost anywhere in central Chicago.
The Art Institute of Chicago is one of the great museums in the world, and well worth a visit.
If you are not afraid to spend some money, watching a Cubs baseball game at Wrigley Field would be a treat. It is probably the last of the truly intimate old ballparks, and the experience is very different from that in large, modern stadiums.
Enjoy your stay, Alberto!
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