From Hill, 1973:

"Clemens' concerns over Olivia's health led him to rent a cottage in York Harbor, Maine, for the summer, where she was transported on Henry Rogers' yacht in late June."

From Hill, 1973

"...the Clemens family loved the house at Riverdale (later known as "Wave Hill" and occupied by Arturo Toscanini and Sir Gladwyn Jebb, British ambassador to the United Nations). It was an enormous fieldstone, three-story mansion with impressive wooded grounds, just inside the New York City limits."

Sam returned to New York May 10th, 1901, where he signed a lease indenture for a cottage that he would name “The Lair” (it would later be called “Mark Twain Camp”) on Saranac Lake, N.Y. The lease to run from June 1 to Oct. 31, 1901 for a total of $650, with $150 at the signing and $250 on July 1 and $250 on Aug. 1. Sam and George V.W. Duryee, owner of the Adirondack Park Co. signed, with Olivia L. Clemens signing as witness.

November 3-5, 1900: The Clemenses visited with William Dean Howells and Laurence Huttons in Princeton, NJ

From November 10th DBD Entry:

The world does move! Mrs. Clemens & the girls have gone off in a hired mobile to the theatre in Harlem. She & I went to Harlem in a coupe three days ago, with a poor tired horse who made less than 4 miles an hour, & it is a pity for the horse that has converted the woman.

Now then, please tell me where in New York we can send & get a mobile at peace-rates when we need one [MTP].

The Clemens family returned to the United States believing that Jean could receive proper treatment in New York City.  They sailed on the Minnehaha.

From the New York Herald, October 15, 1900:

I left these shores, at Vancouver, a red-hot imperialist. I wanted the American eagle to go screaming into the Pacific. It seemed tiresome and tame for it to content itself with the Rockies. Why not spread its wings over the Phillippines, I asked myself? And I thought it would be a real good thing to do

On May 10, 1899, Sam wrote in a letter, "We shall reach London May 31, by way of Bremen & the steamer “Lahn” to Southampton.

David Fears wrote (for the August 3, 1899 entry) of  a letter to Rogers: "I am unspeakably sorry to lose the steam yachting and the Fairhaven visit, and I wasn’t expecting to lose the whole scheme, but the Swedish project made a sudden and radical change in our plans. You see, Jean’s health has made no real and substantial progress in the past 3 years. None whatsoever. We had tried the baths, and the doctors and everything—all no good. What should we do? For one, I was willing to try anything that might turn the tide— except Christian Science.

...

Mark Twain stayed in Vienna with his wife Olivia and his daughters Clara and Jean from the end of September 1897 till the end of May 1899, except for a few weeks in the summer of 1898, spent at the summer resort of Kaltenleutgeben near Vienna.

The family took quarters in Hotel Metropole, beautifully situated on the Franz-Joseph's Quay, on the right bank of the Danube Canal.  Later they moved to the Hotel Krantz, opposite the old Capuchin Church and Monastery, in the center of the city.

Sam’s notebook:

Sund, July 25. At 6 this am, for the first time in the week, sun & surface were just right for mirror-effects—so the lake was full of pictures.

Twain spent his time in England working on his book, Following the Equator.  Isaac Gewirtz, Mark Twain A Skeptic's Progress  pg 87-9, writes of this: