First Methodist Church, Evanston, IL
I don't have documentation that this is where the Twain-Cable speaking engagement occurred but the Twain Speaking Engagements site mentions it occurred in the Methodist Church and Janet C. Olson
Assistant University Archivist at Northwestern University Library provided me with the address:
"I noticed on your website a passing mention of a Methodist Church. That would make sense--in 1885, the largest venue that the University could have used would have been the First Methodist Church (built 1872, used until 1909, and located at 1630 Hinman Avenue, Evanston). ....other options would have been University Hall, or else the original Old College building--possibly the gymnasium building." (email correspondence).