Amtrak Amtrak travels to more than 500 destinations around the country, with 40 trains arriving or departing from Union Station each day. If you want to make getting there part of your trip, keep in mind that Amtrak will take you to nearby cities such as St. Louis, Springfield, Illinois, Indianapolis, Madison, Wisconsin, and Milwaukee in just a few hours. The rates can be comparable to flying if you book well in advance, but unlike most airlines, Amtrak offers the option of sleeper cars for long trips, where you can let the rhythm of the train rock you to sleep.   Chicago's Amtrak hub is part of Union Station.   The Amtrak ticket counter is located on the ground level between the concourses. Trains leave from both the North and South concourses, and well-wishers can accompany passengers all the way to the platform for mushy, Hollywood-style farewells. Travelers with laptop computers can plug in to phone jacks located in one of the two large Amtrak lounges (located across the corridor from the ticket counter). Here, people can send faxes or check e-mail, as long as they are dialing a local number. Reservations for riding Amtrak can be made by phone at (800) 872-7245, on their Web site or through a travel agent. You can also buy your ticket in advance at the counter. Personal checks and major credit cards are accepted. Photos: Steel Bokhof