Pushcart Coffee is a recent addition to East Broadway (221 East Broadway), and has an excellent atmosphere. Go there for coffee.
And just next door is Malt and Mold (221 East Broadway), selling cheeses and selections of beer that are guided by quality (imports and domestics, as well as growlers of local brewed beers).
A long known secret of mine since residing in London is that cheese is actually better with ale than with wine, thus elevating the English beyond the French when it comes to pairing cheese with alcoholic beverages. I recommend English ale when pairing your cheese (Badger; Speckled Hen; etc) .
Another secret I discovered while living in London is that Americans have never eaten cheese. Cheese made in the United States is something else, while cheese found in the isles of the UK and Ireland as well as continental Europe, is cheese.
So, go for some coffee, and when you are done, stop into Malt and Mold for real (imported) cheese and domestic artisenal cheese, and beer to take home. Be sure to visit the Jeremy Willis exhibit (until June 1st) at the Allegra LaViola Gallery at 179 East Broadway. His art strikes me as having a bit of Francis Bacon, and perhaps one can discuss that and more over fresh brewed coffee at the Pushcart Coffee.