I don't know any must-go place to eat. I like Latin Quarter where your can find many restaurants along the street. You can dine on the street side. The price is very reasonable. All the restaurant will post their special menus outside. A 3-course meal costs about 10 euros (2010 price).
Pantheon and Jardin de Luxembourg are near by and both are worth a visit.
Latin Quarter is just across the river from Notre Dame.