We stayed in an apartment in the West Greenwich Village which we liked a lot. The west village is not on the grid created in 1811 so the streets go this way and that way which adds to it's uniqueness since most of Manhattan is laid out in a not so organic grid. West Greenwich village WAS a Dutch village at one point and still looks it today.  Greenwich is an anglicized version of the Dutch word Groenwijck which mean Green District.

I would recommend the apartment we stayed in which we rented via airbnb.com - https://www.airbnb.com/rooms/3783231