Trains to Chicago come from all parts of the country -- Amtrak considers Chicago a main hub, and if you look at a national Amtrak map you'll see the lines all feeding into a central spot, Chicago. Even if the cross-country train rider's final destination isn't Chicago, they almost certainly pass through it. Chicago ranks 4th for Amtrak ridership to and from the city, with over 3 million passengers per year. The 5th place destination, Los Angeles, comes in at only 1.5 million.
Some of the busier/well-known routes include the California Zephyr which travels from San Francisco through Denver to Chicago; the City of New Orleans which, as the name implies travels from New Orleans through Memphis to Chicago; the Empire Builder, which travels from Seattle through St. Paul to Chicago; the Lake Shore Limited, which travels from New York through Albany to Chicago.
All Amtrak trains come into Chicago's grand Union Station downtown, a short walk or cab ride to a large number of hotels. Union Station is a tourist attraction in its own right -- the big shootout scene towards the end of the movie The Untouchables was filmed at Union Station. (Movie trivia note: the scene, including its notable "baby carriage on the stairs" moment, was an homage to the Odessa Steps sequence from the 1925 Russian film, Battleship Potemkin.)