Start at the Field Museum of Natural History in Burnham Park (E. Roosevelt Road and S. Lake Shore Drive; $12). There you'll meet Sue, the world's largest and most completely preserved Tyrannosaurus rex.
Then grab a cab to visit the architecturally impressive Tribune Towers (435 N. Michigan Ave.). When you're done, take the stairs down to the Billy Goat Tavern for a $3 "cheezborger"--the inspiration for the famous Saturday Night Live skit.
Back above ground, head north on Michigan Avenue--a.k.a. the Magnificent Mile--for world-class window-shopping. Finish at the John Hancock Observatory (between Chestnut and Delaware). The skyscraper was invented in Chicago, and you'll see some of the finest examples glittering below.