First you will have a great time even without me sharing some very special places that are NOT expensive! I have visited all of these many times and NEVER been disappointed. I will keep it to four!
Lunch: Monmartre area, Le Pubert, around 10-15 Euros for a three course meal. Give yourself at least 2 hours! Just sit and sip on a local pitcher of wine as the food is prepared. See the picture, it is on a street just off of the square, you can't miss it. A mom and pop place, voted the best value in Paris!
Dinner: Relias du Venice, just North of Arch de Triumph, across from the RER station at Rue Maillot. Go Only if you like great steak, it's all they serve, you have three choices, rare, medium or well. Includes a great salad and potato's. This is a favorite of all I have taken, just get there in line early. They take no reservations and open at 7 Pm, you will want to be on the first setting, the line can get quite long! See pictures. Cost around 20 Euros, but really a fun place!
Lastly, this one is my favorite for a snack, and bathroom break just a few yards North of Notre Dame Cathedral (Toward the Seine!). Its Quasimodao's! Just remember to hit the BR, downstairs, as soon as you order, and then I always stop back, when I leave! Fun for a beer or a break.
For that one memorable meal, go to across from the Opera, in the Grand Hotel on the sidewalk for the neat Cafe de L' Paix! See pictures of all four!