If you're visiting NYC, why would you stay outside of the city???
If you must, you could stay on Staten Island and take the free ferry to Battery Park. From there you can take the subway easily to any destination.
Check out Priceline Express Deals for really affordable options in the city. Unless there's a huge event going on, I've found NYC to have extremely reasonable hotel rates.
+1 for Algonquin. A great little hotel with a lot of history in an excellent location.
I've seen the Waldorf Astoria for $100 a night in the not too distant past
