The Quaker City arrived at Horta the morning of June 21, 1867 (?). It departed again June 23, 1867 at 11:00am. [Mark Twain Project: Quaker City Itinerary]
McKeithan, in Traveling with the Innocents Abroad, comments on the date. "In the book Twain says it was early on the morning of June 21 that they first sighted the Azores, but he was probably misled by an entry in his journal beginning thus: 'June 21st, Azores. Daylight. Arrived at the port of Horta' (Mark Twain's Notebook, New York and london, Harper and Brothers, 1935, p. 61). Probably June 21 was the date of the entry, not of the arrival. The same entry mentions the ten-mile ride by jackass and the dinner for eight. Moreover, a brief letter which he wrote to his mother from Fayal was dated June 20 (Mark Twain Letters, I, 129).