Being as TR came in Third its more probable that Henry George would be the winner. That though, brings up a number of potential events, as the largest city in the United States is now run by what at the time is a radical political movement, right in the middle of the Guided Age.
From the viewpoint of the City itself, a radical left party in power is something that could theoretically push the reform minded City Republicans into the arms of Tammany, rather then United Labor. I doubt such a political alliance could last past the 1898 unification of the City but for a decade we could have a rapport between the two parties on Manhattan, one Brooklyn is voting in the same elections we'll see the Republicans begin to move back towards their Proto-LaGuardianism.
As far as administration goes, George and his clique are the leadership of United Labor, but the rank and file of the party came from Trade Unionists and the Urban Poor, there is going to be as soon as the new mayor is sworn in a crisis in the party as Marxists try to expand their influence. That said we can probably see common ground on a few issues, like laws that work to keep Asians out.
Beyond that, I'm not sure how George's theories would be attempted, or how he'll be able to deal with the combined might of the old Conkling Machine, Tammany, not to mention Federal and State governments. More later on that.
As for Teddy Roosevelt, he's going to need a miracle to be a winner here. In New York City the Democrats were on the rise, the GOP wouldn't be viable until the rise of Fusion tickets in the next decade, and wouldn't be able to stand on their own in New York City until well into the Next Century. The Republicans knew this too, and that's why such a young, relatively inexperienced candidate was even the nominee.