During the day, yeah take the L, go to lower Wacker to do the Blues Brother tour. BTW, the mall they drove through is in a S. Suburb, Harvey. Last I checked its still there and still closed, adorned with plywood and graffiti resembling the movie.
I suggested the cab moreso for the nightlife aspect. For instance, Hard Rock is just a mere block or two from alligator gardens, not sure if they closed that project yet. There's several other "bars" of choice that are popular that are around the same area. Back in my youth "no fear" days I repo'd cars and that was not exactly the best of times/areas
Heck its Chi-town, during the day, take a walk you will see much more that way. Plenty of museums: Planetarium, Sci and Industry (coal tour is a must), Art, Shedd aquarium. North side has the usual staples close to Wrigley: Harry Carey's (cool sports bar), the Improv is in the same area, real cool place to go.
There is no shortage of things to do.