Re the place near Father Demo Square: their pumpernickle bagles with sesame seeds, topped with bacon horseradish cream cheese is serious comfort food for me. They have a lot of varieties of cream cheese too.
I agree that Bagels on Hudson are the best in the neighborhood. In addition to the standard offerings, they have true whole wheat bagels, which I love when I'm not in a traditional mood. He also has homemade soup that's really good.