Now if you have any time at all and your a train buff... I would highly reccomend a trip on the "El" for its historic value, plus the great views of the city. The el is unlike any other system I've seen, and it is very much worth a ride! If your just riding the train, you can ride out to a transfer station and back for 1 price (transfer stations being any station that does not require you to exit the turnstiles to reach the Inbound Platform).
Great idea. Boundaries:
Don't ride the Red Line north of Addison (unless you're going to Howard to transfer to the Purple or Yellow);
Don't ride the Red Line south of Cermak-Chinatown (unless you're going to 35th specifically to see Comiskey, or to 95th to get shot by GDs);
Don't ride the Green Line west of Clinton;
Don't ride the Green Line south of Roosevelt (unless you're looking for cocaine);
Don't ride the Pink Line west of Polk;
If you don't want to worry at all about safety or theft, ride the Brown or Orange Lines.