You could go to Les Halles and have a French press coffee. It is excellent and you can have French baguette with it and it is nice in the morning time. There isn't too many people and you can sit outside also if the weather is nice.
There's a place called something like "Brasil Coffee" on Lex and 30th (or maybe 31st). I don't particularly like the coffee, but people definitely sit around there and study/write. Also, espresso drinks are ok; it's just the drip coffee that I don't like.