What would you show/take someone to who is visiting Chicago for the first time - besides things in details?

You've got a good list there. But I'd try to get away from the tourist areas for a while and show him ALL of the city, maybe take a train ride up to Evanston, go hang out in Andersonville, maybe Wicker Park (I personally don't like it but, hey..), the Garfield Park Observatory, Museum of Science and Industry, and a game at Sox Park.