Traveling from Thompsonville to Brooklyn:  New Haven, Hartford and Springfield; New York & New Haven Railroads.  How or where Sam crossed the East River to Brooklyn, I don't know. The NYNH&H stopped at Oak Point.

December 1, 1869:   Bedford Avenue Reformed Church, Brooklyn, New York.

 Sam lectured (“Savages”)  for Brooklyn Library Society, at the Bedford Avenue Reformed Church, Brooklyn, New York. Sam’s lecture schedule allowed him to spend most of Dec. 1 to 6 with Livy in New York City [MTL 3: 428n1].

December 3, 1869:  Collingwood's Opera House, Poughkeepsie, New York

From New York to Poughkeepsie, the Hudson River Railroad.

December 6 - Beecher's Plymouth Church, Brooklyn, New York

The Brooklyn lecture of December 6, 1869 was cancelled due to an apparent misunderstanding.

To the Editor of the Brooklyn Eagle
3 December 1869 • Brooklyn, N.Y.
(Brooklyn Eagle, 4 Dec 69, UCCL 02283)

To the Editor of the Brooklyn Eagle:

I was to have lectured in Brooklyn on Monday, Dec. 6th, but a misunderstanding has intervened, and I take this method of informing the public that I have canceled the engagement, and will not be present upon that [occasion.

Mark Twain.

Brooklyn, Dec. 3d.

“SLC to Ed., Brooklyn Eagle, 3 Dec 1869, Brooklyn, N.Y. (UCCL 02283).” 

By the evening  of this day, Sam was in Boston,  at the annual dinner of the Boston Press Club.  It's possible Twain slept on the train from Boston, back to New York then on Camden and Amboy to Philadelphia.

December 7, 1869: Academy of Music, Philadelphia, Pennsylvania

Between Philadelphia and Washington D.C., Twain would likely have ridden the Northern Central and the Philadelphia, Wilmington and Baltimore lines.

December 8, 1869:  Lincoln Hall, Washington, D. C.

December 9, 1869:  Germantown, Pennsylvania

December 10, 1869: Methodist Church, Mount Vernon, New York

Sam spent part of Dec. 10 and 11 with Livy in New York City [MTL 3: 428n1]