The Chicago Tribune, March 6,1882, p.5
As to venue and accommodation
The Chicago Tribune, March 5, 1999 | Oscar Wilde Well-received In Rockford . . .Again | by H. Lee Murphy. 
"Wilde first became known to Americans during a long lecture tour. Indeed, he stopped to speak one March evening in 1882 at the Rockford Opera House, staying at the old Holland House and dining at the home of a Dr. Thomas Butler, according to the Rockford Daily Gazette account at the time.
The Gazette said that Wilde attracted a small but attentive audience at his Rockford appearance."
 While this is not a primary source in itself, it is the reporting of a primary source, and there is no reason to doubt it