My favorite restaurants in Paris are: Le P'tit Trouquet 28 Rie de'Exposition and it is in the Rue Cler area. I have been there 3 x and it never disappoints! Make reservartions, very small place, not open for lunch.
Les Cocottes - Rue Cler also - 135 Rue St. Dominique -- all the dishes are served in small iron pots. Very nice place, but I will warn you all the tables are high and you sit in high stools. I went for lunch and it was perfect. I would go back for dinner too.
L'Orangerie -- On the Ile St. Louis - 28 Rue St Louis-en-lle reservations needed! Wonderful place, excellent food. Dinner here is perfect.
Brasserie Bouillon Racine - amazing decor sit on the 2nd floor, reservations needed. Most beautiful restaurant I have been to! Art Nouveau decor! 3 Rue Racine I believe it is near the Cluny Museum. Great for dinner
Creperie Josselin67 Rue du Montparnasse Fun and casual place - excellent crepes, best I ever had. You may not like crepes but I can almost say you will love these!!! Nothing else like it. Great for either lunch or dinner.
I will make sure the next time I go back to Paris I will go to all these restaurants and I hope to find more to add to my list. Make reservations and make sure a restaurant is open on a Sunday night as many in Paris seem to be closed. Have a wonderful trip. they may not be the areas that you asked for, but they are ones I have been to and really enjoyed. Let me know if you went to any of the above and if so, did you like them or not. Love to hear your feed back.