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:

In 1863 the Rockford post office was located on S. Main Street what was then the Holland Block. At that time there was no mail delivery and people living on the east side of the river were forced to walk to retrieve their mail. So great was the agitation that several prominent citizens talked of building the post office on West State Street. Finally Horace Brown came forward and said that if he could be assured of the post office he would build a structure to house it. This assurance was given and the construction was begun. When the building was completed Mrs.

Built at a cost of $60,000, the top two levels of the Metropolitan’s three stories were devoted to its 1200-seat theater, while the street level featured storefronts, a cagey hedging of bets on the part of Butsch. Other theater managers struggled with low attendance and protests by local clergy of the “immoral character” of the theater, so Butsch called his establishment a hall, rather than a theatre.

Hamilton's hall erected on the site of the Rurode Dry Goods Company building on Calhoun street .

The location of Mark Twain's lecture in Akron, OH on December 30, 1868 is noted as the Methodist Church.  The location and name of the site in 1868 has not been definitively determined but one possibility is ...

The Universalist's Old Stone Church is gone, but the Sojourner Truth
Building in its place is named for an event that put Akron on the civil-rights map.

In 1811, Paul Williams settled near the corner of what is now Buchtel Avenue and Broadway. He suggested to General Simon Perkins, who was surveyor of the Connecticut Land Company's Connecticut Western Reserve, that they found a town at the summit of the developing Ohio and Erie Canal.

Although I have found no documentation on just where Mark Twain delivered his lecture, December 26, 1868, it seems likely it was somewhere within the historic district.

The Tecumseh Downtown Historic District is a historic district comprising the downtown commercial area of the city of Tecumseh in Lenawee County, Michigan. It was designated as a Michigan Historic Site on January 16, 1976 and added to the National Register of Historic Places on April 17, 1986.