I am unable to find a location for this site although I have found references such as "Library Hall and Reading Room in Joy's marble-building on Lake Street". There was on Lake Street:
The Wigwam was a convention center and meeting hall that served as the site of the 1860 Republican National Convention.[1] It was located in Chicago, Illinois at Lake Street and Market (later Wacker Drive) near the Chicago River.[2] This site had previously been the site of the Sauganash Hotel, Chicago's first hotel.[1] This is where supporters ushered Abraham Lincoln to the party nomination and the eventual U.S. Presidency. The location at Lake and Wacker was designated a Chicago Landmark on November 6, 2002.[1] The name "Wigwam", although separate structures, was later associated with host locations for both the 1864 Democratic National Convention and the 1892 Democratic National Convention in Chicago.