Note: Carson's is no longer on State Street, they left a few years ago.
You can easily take the bus from Michigan Avenue and go on South Michigan to get to State Street (#3 King Drive, #151 - the bus drivers will help you out if you are unsure). There is a Nordstrom's Rack on State Street, H&M, Sears and Macy's (the old flagship Marshall Field's store), plus new shopping at the old Gallery 37 area.
If you are going to eat on Michigan, I would advise not eating at a chain restaurant. There are many great places to eat. If you let me know your specific interests, I can recommend some places in all price ranges.
Have a fun trip!