Possibly misidentified, this location my actually be North Hall.  North Hall was constructed in 1865, to be used, in part, as a University Chapel. The original recommendation, made by Governor Samuel Kirkwood, requested funds for a chemistry laboratory, chapel and astronomical observatory, and over the years, North Hall, the two-and-a-half-story, red-brick classic, certainly became a multi-use facility.

I found references to three Methodist Churches in Ottawa, IL but found no mention of dates for their structures.  The First United Methodist Church at 100 West Jefferson Street, Ottawa, IL 61350 is closest to downtown Ottawa

William, who never actually lived in Decatur, was the first Powers to start building commercially. After purchasing farmland in rural Macon and McClean counties, in 1856 he turned his attention to the city, constructing a group of buildings in what became known as Powers Block — the south side of 100 block of East Main. Among those buildings was Powers Hall, which housed Decatur’s first auditorium.

Dr. Rudolphus Rouse's Performance Hall was located at the North West corner of Main and Jefferson Streets, and played host to many theatrical and opera companies. It was called "Main Street" theater after 1902. 

http://collections.carli.illinois.edu/cdm/ref/collection/bra_peoria/id/1

I have found no documentation indicating the name or location of Mark Twain's lecture in Galesburg.  Yet Galesburg does have an appropriate site: