Try Hawthorne Valley at the Union Square Farmers Market. Their Cheddar (medium and sharp) is quite good. http://www.hawthornevalleyfarm.org/
The Grand Army Plaza Farmer's Market (on Saturday) would be even closer. Cato Corner Farms has excellent cheeses. http://www.catocornerfarm.com/
I've never made cheese before, so unfortunately, I can't help you with finding fresh curds.