There are tons of grocery stores in the West Village. The best part is that several are natural and organic grocery stores. You're also only a few blocks from the farmer's market (Mon, Wed, Fri and Sat) which is a huge plus. I consider it a little village or a mini London. It's one of the best areas to live, truth is I think it's the best as you are a skip away from Meat Packing, Soho, East Village, Tribeca, Gramercy - all walking distance. Also if you're into Organic, it's one of the best areas to find organic restaurants or organic juice bars.
Good luck with your search!
Rental and Sales agent