The family finally left for Elmira and Quarry Farm on June 15, 1880, and railed to New York, where they overnighted at the Gilsey House.
... the next morning the clan entrained for Elmira in a special sleeping car Sam hired because Livy, now almost eight months pregnant, needed “to lie down a good deal.” Had they not had an entire car to themselves, Sam reckoned, “Livy & the children would have found the ten-hour trip wholly unendurable, This is the first time Livy ever made that trip without arriving in a played-out condition. She shall always go by special car hereafter, until we bust.” After a couple of weeks with Livy's mother at the Langdon mansion on Main Street, the Clemenses moved up East Hill to the farm.
...
Jane Lampton Clemens (aka Jean), named for Sam’s mother, was born at Quarry Farm on July 26, Livy's doctor Rachel Brooks Gleason and Sam were both initially concerned about the health of the new mother, though she was soon out of danger. He announced to his sister Pamela that at about seven pounds Jean was “as fat as a watermelon, & just as sweet & good, & often just as wet,’ and he reported to Howells that she “arrived perfectly sound but with no more baggage than I had when I was on the river.” She was ‘the prettiest & perfectest little creature we have turned out yet. Susie & Bay [Clara] could not worship it more if it were a cat.” ...
[From page 314 The Life of Mark Twain - The Middle Years 1871-1891
July 9, 1880: Approximate date Sam moved to Quarry Farm from Elmira, as per letter to Twichell dated July 19.
July 26, 1880: Jean is born at Quarry Farm
August 3, 1880: Possibly the most important historical event to occur in Elmira, at this time, was the Emancipation Day celebration. Matt Seybold notes that “Twain never directly commented upon the event in his public or private writings.”. Seybold does, however, present a strong argument for Twain’s presence at Douglas’ speech. (EVEN IF HE WEREN’T MY FRIEND: FREDERICK DOUGLASS & MARK TWAIN,)
See To James A. Garfield 12 January 1881 • Hartford, Conn.
The Day By Day entry for this date is only a quote from Lighting Out for the Territory, Reflections on Mark Twain and American Culture By Shelley Fisher Fishkin · 1998:
“ August 3 Tuesday What Fishkin calls “noisy hoopla that engulfed Elmira” was the arrival and speech of Frederick Douglass. “The event drew delegations from virtually every city and town within a hundred miles. Sixty-three guns were fired at 11 A.M. Well before the parade began, the ‘excitement reached the white folks, and the streets were thronged with expectant people.’” At least four bands provided music. The parade route went around the Langdon home. Even if Sam were up on Quarry Farm, he would have heard the commotion [Lighting Out 95-6]."
September 27, 1880 – The Clemens family left Quarry Farm and Elmira and took the special “hotel car” for the ten hour ride to New York City, where they stayed three days at the Gilsey House.
Matt Seybold makes an interesting observation of Mark Twain's character at this time:
Twain was, quite clearly, grappling with the legacy of the South, which was his own legacy. He still sometimes (selectively) introduced himself as a Southerner, and frequently traded upon this identity in his humor and personal branding. But it is hard for him to face the truth. His first, rejected estimation of Southern celebrity could easily have been ripped directly from Douglass’s own descriptions of the ingrained and degrading culture of violence in the South. But he is not fully comfortable, even in his private journal, with naming that culture of violence, though his representation of it was already starting to take shape in the manuscript of Adventures of Huckleberry Finn he had been working on earlier in the Summer of 1880.