There are a variety of volunteer opportunities in the Chicago area and a variety of ways to search for the opportunity that meets your needs.
http://www.volunteermatch.org/bymsa or http://www.chicagovolunteer.net/ are excellent search tools for volunteer opportunities. In addition, there are some long-standing organizations with excellent volunteer placement:

The Junior League of Chicago (JLC) (1447 N. Astor Street, Chicago, IL 60610 Tel: (312)664-4462 http://www.jlchicago.org/jlc/)
Founded by Lucy McCormick Blair in 1912, this group focused on developing the potential of women as trained volunteers, overseeing a multimillion-dollar budget and 1,500 members. Each year, Junior League volunteers donate more than 200,000 hours to the community. In addition, the JLC raises thousands of dollars each year for community projects.

Girl Scouts of Chicago (222 S. Riverside Plaza, Suite 2120, Chicago, IL 60606 Tel: (312)416-2500 http://www.girlscouts-chicago.org/)
Offers opportunities to mentor groups of young girls for character development. This includes offering your own skills for youth to learn as well as chaperoning the group during outings. Other volunteer positions include helping the organization with marketing, conducting workshops, and developing curriculum.

McCormick Tribune Freedom Museum (435 N. Michigan Ave, Chicago, IL 60611 Tel: (312)222-4860 http://www.freedommuseum.us/)
For a chance to participate in a museum atmosphere, McCormick Tribune Freedom Museum offers excellent positions. Greeting guests, conducting tours, and sharing history are all part of the activities. This is a chance to interact with all kinds of people about current events, history, and freedom.

Esperanza Community Center(520 North Marshfield Avenue, Chicago, IL 60622 Tel: (312)243-6097 http://www.esperanzacommunityservices.org/)
Volunteering at Esperanza Community Services is very rewarding. You can volunteer for one of our special events or help with painting classrooms and gardening. The mentoring program allows our students to build positive relationships with adult role models while participating in activities that develop their social and vocational skills, and helps them build self esteem by giving back to the community.