Don't know the name of either place, but:
Cuban Sandwich - A deli on the south side of Fulton Street halfway between Broadway and Nassau and right across from the Lucille Roberts. (Right now, it's partly hidden by scaffolding.) Great cuban sandwich with tender moist pulled pork. Huge, too, for only around $5.
Korean place- in the Nassau subway station has good, quick Korean food. Bibimbap was particularly good, although they give you a sauce that's a bit too sweet unless you ask for the spicy stuff.