The election calendars, nominations, and candidates for these offices are managed by the New York Secretary of State Elections Division. The actual elections, as with local elections, are managed by county election commissions. These offices include the federal positions of President of the US as well as state-specific offices such as Governor and Senator.
The state manages campaign-finance reporting for state-specific offices, while campaign-finance reporting for the federal office of President is managed by the US Federal Election Commission.