Michelle L.,
I found these two newspaper articles stating where Drayton was renting homes during 1902. I hope they help. I will see what other information I might find.
Michelle E.
The summer of 1902, James and his daughter Caroline rented a summer cottage in Isleborough, Maine.
"About People and Social Incidents," New-York Tribune, Wednesday 30 April 1902, page 8, column 6. Newspapers.com : accessed 13 October 2018.
That winter, they rented the home of General di Cesnola, on East 57th Street.
"About People and Social Incidents," New-York Tribune, Wednesday 10 December 1902, page 6, column 6. Newspapers.com : accessed 13 October 2018.