I feel that NYC mayors frequently overestimate their appeal to the rest of the country... remember how bad Rudy flopped when he ran? And that guy may have been NYs most famous mayor ever.
New York Mayors aren't as bad as New York Governors and Senators at the Presidential level, only recently have Mayors thought it made them national material by itself. New York in general has a losing record, and even that's propped up by FDR. Using "primaries" here to also mean conventions and caucuses.
Mayors:
John Lindsay (lost primaries... also Representative)
Rudy Giuliani (lost primaries)
Michael Bloomberg (tbd)
Bill de Blasio (lost primaries)
Governors, Senators, etc.
Governors:
George Clinton (lost primaries, became VP)
Horatio Seymour (lost election)
Samuel Tilden (had rigged election stolen from him)
Grover Cleveland (won presidency, lost re-election, won election again)
Theodore Roosevelt (became VP, president killed, won re-election, lost primaries, lost third-party bid)
Charles Evans Hughes (lost election)
Al Smith (lost primaries, lost election, lost primaries)
Franklin D. Roosevelt (won election, won re-election, won re-election, won re-election)
Thomas Dewey (lost primaries, lost election, lost election)
Averell Harriman (lost primaries, lost primaries)
Nelson Rockefeller (lost primaries, lost primaries, lost primaries, became VP)
Hugh Carey (lost primaries... also Representative)
George Pataki (lost primaries)
Senators:
Aaron Burr (became VP, tried for treason)
Rufus King (lost election)
DeWitt Clinton (lost a one-issue campaign... also Mayor of NYC, also Governor)
Martin Van Buren (became VP, won presidency, lost re-election, lost primaries, lost third-party bid... also Governor)
William Marcy (lost primaries... also Governor)
William Seward (lost primaries... also Governor)
Roscoe Conkling (lost primaries)
David Hill (lost primaries... also Governor)
Royal Copeland (lost primaries)
Robert Kennedy (lost life)
Hillary Clinton (lost primaries, lost election)
Kirsten Gillibrand (lost primaries)
Representatives:
Millard Fillmore (became VP, president died, lost primaries, lost third-party bid)
Horace Greeley (lost election so bad he died)
Shirley Chisholm (lost primaries)
Jack Kemp (lost primaries)
Chief Judge of Court of Appeals:
Alton Parker (lost election)
Collector of the Port of New York:
Chester Arthur (became VP, president killed)
New York has had five "major" non-office candidates, they've done better in general actually:
Wendall Willkie (lost election, moved to Indiana)
Richard Nixon (moved from California, won election, won re-election, forced to resign by the CIA)Steve Forbes (moved from New Jersey, lost primaries)
Al Sharpton (lost primaries, moved to MSNBC)
Donald Trump (won election, moved to Florida)Andrew Yang (lost primaries)
Three dudes account for eight of New York's eleven presidential wins. They went 8-1. The rest have combined for 3-13. I didn't count Tilden either way. New York's had a superior rate at getting to the Presidency through the President dying, they've got three of them (Fillmore, Arthur, Roosevelt) which is more than any state.
edit: New York seems to be increasing in "serious" candidates as it's become less of a swing state. That was one reason it used to get VP slots. That actually makes me wonder about nominated candidates and swing states in general. McCain is the only one so far this century actually. Massachusetts (twice), New York (twice in the same election), Illinois, and Texas have been the sources of nominees otherwise. Vermont isn't a swing state. Minnesota is kinda not one either.