This site has not been specifically cited but based on dates opened this is likely the site visited by Mark Twain in 1868.

This was one of the legendary Newark showplace addresses at the busy corner of Halsey Street and Market Street. Opened in 1847, this location served 75 years of entertainment including live music, legitimate theatre, vaudeville, and movies. Beginning as Waller’s Opera House, Fred Waldmann took on the location changing it to Waldmann’s Opera House. The location would move to presenting vaudeville.

The Rondout Social Maennerchor was formed on February 22, 1868, by a handful of German immigrants who loved choral singing. They were drawn together by their common language, and love for music, singing, and social activities so that their clubhouse, "Washington Hall", became a gathering place for similar organizations up and down the Hudson River.

http://www.ghf-nj.org/Kingston.htm

t is unknown if this is the location of Mark Twain's lecture.  A literature search has so far failed to uncover another theater at this date.

The Building and Site. The structure was erected in 1867 at a cost of $89,000. It seated 2,000 persons. It opened on December 17, 1867, with a temperance lecture. Later it was sold and remodeled; it reopened as the Lyceum Theatre in 1898. In 1904 it was lost in a cataclysmic fire that claimed one additional theater and six stores in downtown Elmira. The theater was rebuilt and opened, still as the Lyceum, in 1905. It closed in 1926 and was demolished in 1949.

Westminster Hotel, cor. of Irving Place and 16th St. New York Roberts & Palmer Prop

From Explanatory Notes:  

The original building on the site was Irving Hall, which opened in 1860 as a venue for balls, lectures, and concerts. It was also for many years the base for one faction of the city's Democratic Party.