I can’t see the Democrats letting her keep that office as she isn’t from the NYC area. The most likely candidate would be Tish James. In many ways James is worse than Cuomo in so far as she is an political ideologue whereas Cuomo is a political opportunist.
Senator Alessandra Biaggi’s name has been floated as a candidate for higher office, possibly for Lieutenant Governor. Another ideologue, a James-Biaggi ticket would be bad for just about everything including 2A rights.
As awful as Cuomo’s behavior has been and as destructive as “progressive” policies have been for the state, I don’t see Republicans being in a position to capitalize on any of it in New York. On the national level I think the GOP has plenty of opportunities for advancement especially if they stand firm against any gun control.