Chicagoans have a maddening habit of referring to some expressways by their names, not the numbers used to identify them on the signs you'll see posted on the U.S. interstate highway system, so you'll have to commit both name and number to memory.
I-55 (the Stevenson Expressway) will take you directly from St. Louis into downtown Chicago. I-90/94 (The Dan Ryan) comes in from Indiana to the east (via the Chicago Skyway and Bishop Ford Freeway) and from central Illinois (via I-57). I-90 (The Kennedy) comes in from Madison to the northwest. I-94 (the Edens Expressway) comes in from Milwaukee to the north, but recent roadwork has slowed traffic considerably compared to I-90. I-80 will get you to the city from Iowa which neighbors Illinois to the west.
If arriving downtown from Indiana, from the south on I-94 or I-90, or from the north, Lake Shore Drive (U.S. Highway 41) provides a scenic introduction in both directions, day or night. If arriving on I-55 from the southwest, or on I-290 (the Eisenhower Expressway, formerly and sometimes still called The Congress Expressway) from the west, the skyline may also be visible from certain clear spots, but without the shore view. It should also be noted that I-55 from the southwest and I-90 through much of northwest Indiana are chock full of heavy industries with odors that'll knock your socks off, so plan your route downtown wisely.