The first citation in the New York Times is September 30, 1921, pg. 22. There are several citations of "hizzoner" in the Kansas City (MO) Star of 1880, where "hizzoner" probably meant "his honor," the judge.
20 September 1880, Kansas City (MO) Star, pg. 4:
A Good Day for Business in Hizzoner's Castle.
25 August 1882, St. Albans (VT) Daily Messenger, "Fact and Fancy," pg. 4:
The mayor of Chicago is always referred to by one of the papers there as "Hizzoner, the mayor." This, in Chicago, is supposed to be too awfully funny for anything, and the people there nearly kill themselves laughing every time they see it. -- [Philadelphia News.
12 December 1882, Fort Wayne (IL) Daily Gazette, pg. 6, col. 2:
An old lady from the country was taken in out of the wet, yeesterday afternoon, and with permission of Hizzoner will return home today.
26 May 1883, New Orleans (LA) Daily Picayune, pg. 4:
"Hizzoner" is Mayor of Chicago, according to the Chicago Herald.
2 July 1883, Decatur (IL) Daily Republican, pg. 1, col. 2:
"Love is a most beautiful and ennobling problem," said Hizzoner, the mayor.
("Long" John Wentworth, the mayor of Chicago -- ed.)
4 August 1885, New York Commerical Advertiser, "Chicago as a Model," pg. 2, col. 3:
"Hizzoner," as the mayor is playfully called by the wild Western papers of his municipality (Carter Harrison of Chicago -- ed.), is attacked from time to time by the effete eastern notion that the "gamblers must go?" The police are "peremptorily ordered" to see that all gambling places are closed, but there has never yet been evidence to show that they were closed much longer than it took the ink to dry on "Hizzoner's" orders.