Lunch between 59 and 42 on the east side, preferably between lex and 5th
Slightly outside your boundaries, but on 41st and Madison is Cafe Zaiya which is a super budget friendly cafeteria style Japanese place. It's great! There are lots of different options such as rice bowls with marinated beef or tofu, bento boxes, sushi, tossed salad bar, noodles to order, hot food and best of all, a Beard Papa!
Since I work within that area of Manhattan and often have to make lunch reservations, I use opentable.com to find places based on location, cuisine and price. Some of the swankier places that leap to mind are:
For the more budget-conscious:
You can also use something like seamlessweb.com to search based on your zip code and peruse the delivery menus.