The Interborough Express is one example. Going from southern Brooklyn on the water up to queens. Previous proposals had it also connecting to the Bronx. If you want to be really ambitious, connect Bayridge to Staten Island and continue on with branches to Elizabeth and Bayonne. Up north, it's surprising there isn't rail from the Bronx, through Manhattan, across the GW Bridge to NJ.
https://en.wikipedia.org/wiki/Interborough_Express