From June 21 to June 27, 1891, Sam was in Annecy. I have found no direct mention of where the Clemens' were while at Haute-Savoie but it is possible they tried the Thermes de Sant Gervais Mont-Blanc. From June 27 to July 27, 1891, he was at Aix-les-Bains. Scharnhorst reports they departed for Geneva on the 28th.
Scharnhorst (pg 5) notes "Between hydrothermal treatments he and Livy loitered in the casino, ...They also cruised around Lake Bourget and railed to the medieval villages of Annecy and Talloires ..." On these side trips they "stepped from the sparkling water and the rush and boom and fret and fever of the nineteenth century into the solemnity and the silence and the soft gloom and brooding mystery of remote antiquity.""
AIX-LES-BAINS. Certainly this is an enchanting place. It is a strong word, but I think the facts justify it. True, there is a rabble of nobilities, big and little, here all the time, and often a king or two; but as these behave quite nicely and also keep mainly to themselves, they are little or no annoyance. And then a king makes the best advertisement there is, and the cheapest. All he costs is a reception at the station by the mayor and the police in their Sunday uniforms, shop-front decorations along the route from station to hotel, brass band at the hotel, fireworks in the evening, free bath in the morning. This is the whole expense; and in return for it he goes away from here with the broad of his back metaphorically stenciled over with display ads., which shout to all nations of the world, assisted by the telegraph: Rheumatism routed at Aix-les-Bains! Gout admonished, Nerves braced up! All diseases welcomed, and satisfaction given or the money returned at the door!
(AIX, THE PARADISE OF THE RHEUMATICS)
On Twain's excursion to Annecy: At the end of an hour you come to Annecy and rattle through its old crooked lanes, built solidly up with curious old houses that are a dream of the Middle Ages, and presently you come to the main object of your trip — Lake Annecy. It is a revelation. It is a miracle. It brings the tears to a body’s eyes. It is so enchanting. That is to say, it affects you just as all other things that you instantly recognize as perfect affect you — perfect music, perfect eloquence, perfect art, perfect joy, perfect grief. (DBD July 19).