One of my favorite breakfast spots in midtown is Certe (on 55th btw. Madison & Fifth), takeout in the front and a hidden, sweet little dining room in the back, where they also prepare catering orders. Great if you want a step up from a coffee shop but not too fancy, great breakfast specials and home-baked goodies... FWIW, I really dislike Pershing Square, crowded and not very good food.
Ma Peche serves breakfast but doesn't have a menu online; you may need to email to find out.
db bistro moderne also serves breakfast.
If you can go down to 37th, Ai Fiori may be an option.
DB Bistro Moderne
55 West 44th Street, New York, NY 10036
15 W 56th St, New York, NY 10019
400 5th Ave, New York, NY 10018