The Troy Savings Bank was founded in 1823 and moved to its current location in 1870. In appreciation of the community's support, the plans for the new building called for a music hall to be built on the upper floors. In the early years of the 20th century the Music Hall featured performances from artists such as Lillian Nordica, Henri Vieuxtemps, Ignace Jan Paderewski, Albert Spalding, Sergei Rachmaninoff, Myra Hess and Jose Iturbi. In the 1930s and 1940s, artists including Vladimir Horowitz, Yehudi Menuhin and Artur Rubinstein played there.

The local newspaper of record in the 1880s was the Jerseyman. I searched the Friday after Thanksgiving in 1884 but failed to find an article about Twain and Cable speaking here or staying with Thomas Nast. However, I found the following brief article on the previous Friday, the 21st an page 2 at the bottom of the 4th column: 

10th & G St NW, November 24 & 25, 1884 and February 28, 1885, the final show of the tour. 

in May 1868, the congregation moved into its new home at 10th and G St. NW. Its large brick building made a statement. The Congregationalists were here to stay.

The Brooklyn Academy of Music (BAM) is a major performing arts venue in Brooklyn, New York City, known as a center for progressive and avant garde performance. It presented its first performance in 1861 and began operations in its present location in 1908.

I needed DuckDuckGo to find this location.  http://www.philadelphiabuildings.org/pab/app/pj_display.cfm/8304 

Image from: http://www.phillyhistory.org/PhotoArchive/MediaStream.ashx?mediaId=32523 

November 21, 1884 and November 26th (two shows).

November 20, 1884 

"From the daughter of Francis N. Bain, 1st proprietor, we have the following authentication: Mrs. John Nolle (Francis Bain Nolle) reminds us that the early Opera House on 2nd Street, just east of the hotel and the Academy of Music, on Broadway, west of Grand Street, supported interesting plays and singers. In fact, many of the plays that were to run on Broadway in New York City had try-outs in Newburgh. Also, Newburgh on the circuit of the early producers tours." 

The firm also ran the "Chickering Hall" concert auditorium in New York City at no.130 Fifth Avenue, 1875-1901. The building was situated on the north-west corner (not north-east contrary to some sources) of Fifth Avenue and West Eighteenth Street, and was the venue for Oscar Wilde's first lecture in America. [Source: New York 1880: Architecture and Urbanism in the Gilded Age, Robert A.M. Stern (Author), Thomas Mellins (Author), David Fishman (Author)].  http://en.wikipedia.org/wiki/Chickering_and_Sons

Through the years there were eight theaters in Plainfield. The Stillman Music Hall (216 W. Front Street) was built in 1884. Its entertainments included plays, lectures, concerts, operas, minstrel shows and variety stars until it closed in 1901.  http://www.plainfieldlibrary.info/OnlineExhibits/LBNF/Theaters.html

November 14, 1884 

Mark Twain had complained that there was not enough notice of this event to generate a suitable audience. Here is the text from the notice published in the Brockton Enterprise, November 1, 1884: \

"OPERA HOUSE.--M.W. Hanley's company, presenting Harrigan & Hart's play, "Dan;s Tribulations," will be at this house November 6th. Nov.9th the Flora Myers company return for a season of dramatic representations at popular prices. The 14th Mark Twain, the humorist, and Mr. George W. Cable, the novelist, will appear in a lecture and readings."