The rise in sea level is something of a misnomer, because the real damage comes in storm surges. Even a 1cm rise increases the amount of water that can pushed inland by *checks notes* a whole helluva lot. So while manhattan isn't going to be put underwater even after a whole foot of sea level rise (predicted by 2100), the storms it has to survive will be much worse.

People won't move just from a little water in the roads (just look at Miami), I think even in the year 2099 you'll have a hard time getting new yorkers to move to ohio, but once a storm comes through and destroys their housing they will have to find somewhere else to live.

Housing is super expensive for people now. All of that coastal infrastructure will need to be rebuilt.