The Chicago Greeter service is a must-do for first time visitors AND those who've been here before.   Visitors in groups from 1 to 6 people are taken to the neighborhood of their choice by a volunteer and given a tour by someone who lives in Chicago and loves their city.  It is a free service and bus or train passes are provided.  This is a great way to either be introduced to the city and transportation system or to see a neighborhood you'd probably never see on your own.  To see a list of possible neighborhoods and to get more details, go to their  TripAdvisor listing page or their website.