This is a good story, but something about it made me want to check snopes. Instead, I went to Stanford's site, and found this story doesn't quite mesh with the official one:
The family was in Italy in 1884 when Leland contracted typhoid fever. He was thought to be recovering, but on March 13 at the Hotel Bristol in Florence, Leland's bright and promising young life came to an end, two months before his 16th birthday.
Stanford, who had remained at Leland's bedside continuously, fell into a troubled sleep the morning the boy died. When he awakened he turned to his wife and said,
"The children of California shall be our children."
These words were the real beginning of Stanford University.
The Founding Grant
The Stanfords returned to America in May and, before proceeding to Palo Alto, visited Cornell, Yale, Harvard and the Massachusetts Institute of Technology. They talked with President Eliot of Harvard about three ideas: a university at Palo Alto, a large institution in San Francisco combining a lecture hall and a museum, and a technical school. Asked which of these seemed most desirable, Eliot answered, a university. Mrs. Stanford inquired how much the
endowment should be, in addition to land and buildings, and he replied, not less than $5 million. A silence followed. Finally, Mr. Stanford said with a smile, "Well, Jane, we could manage that, couldn't we?" and a grave Mrs. Stanford nodded her assent.