We are staying in an apartment across from Notre Dame about a 5 min walk from Shakespeare & Co book store. (Latin Quarter near Place Maubert) We would like to know if anyone has visited any non-touristy restaurants, cafes or bistros in this area that serves good value food. We are very adventurous eaters. We have a few select restaurants that we want to visit that are in 8th, 9th and 10th arrondissements (35mins public transport for most of them). Would like a few 'close to our apartment' options as well. We will be in our apartment for 9 nights so will also probably cook dinner in for 2 or 3 nights if we come across some produce that grabs our fancy. We will eat out for all lunches. Hoping some regular visitors to Paris have some suggestions. We are also thinking of visiting Le Volcan near Rue Mouffetard as we're sightseeing in that area on day 2.
At Notre Dame you're in peak tourist area. There won't be any "non-touristy" restaurants or bistrots. There may be a few that look like it, but a Parisian wouldn't recognise it as such, It's not an area known for authenticity.
If you really want “non-touristy” (even though you, yourselves, are tourists) go to Place de la Nation and all the streets that radiate from it. Or the streets around Bastille. Or Rue des Martyrs in the 9th, not lacking tourists but lots of good restaurants that area residents patronize.
Edit Or rue Grenelle in the 7th
This is generally a hard one since as the original posters have pointed out, this is a pretty tourist-focused area, somewhat the equivalent of asking for non-touristy restaurants around Times Square in New York or Covent Garden in London).
I'd point out the Odéon location of Breizh Café, about a 12-minute walk from Shakespeare & Company as a possible option -- it's not so much that it is "non-touristy" (you will almost certainly see other travelers eating there as well) but that it is indeed good-quality food for the prices you pay, unlike many of the other restaurants in the tourist heart of Paris.
If I can give an "anti-recommendation," avoid anything on rue de la Huchette -- it's the epitome of tourist-centered businesses and I'd suspect that the percentage of repeat diners at these restaurants are quite low, hence there's not really a large incentive for high-quality food.
We were just in Paris this past weekend and enjoyed our dinner at Brasserie Balzar in the 5th on rue des ecoles. I'm not sure if that counts as non-touristy or not, but we liked it.
We loved Le Loubnane, a Lebanese restaurant in that area. You can reserve on www.LaFourchette.com, the French version of The Fork.
Au Bougnat is very good restaurant near Notre Dame. I have been there so I know it is not tourist free but it did not seem touristy. http://aubougnat.com/
Not sure about the touristy aspect since that is, quite plainly, a very touristy area. Having said that, on the main street that runs down the center of Ile Saint - Louis are several places to check out. If you are not having breakfast at the hotel there is a corner place named St. Regis. Coffee, croissant, and juice for very little money. Even had a small plate of cold cuts and wine one evening. On the same street is Café Med which is good for lunch. Farther down the street is L'Orangerie & Auberge de la Reine Blanche which is good for a semi fancy dinner. Reservations are a good idea. And don't miss the chocolate ice cream which is in the same block (other side of the street) from L'Orangerie.
You can't get non-touristy in tourist central but you can get good versus awful -- and yes there are lots of mediocre and bad restaurants in Paris, often in touristy areas. Some restaurants we have had good luck with in this general area are: La Tour d'Argent (very expensive, reserve), L'Initial (54 for elegant and tasty 7 course tasting menu, also reserve; in the 5th near the river), La Cordonnerie (in the 2cd near the Tuilleries, also reserve, lovely little one chef place). We have also eaten at Balzar and it was decent too. The Rotisserie Tour d'Argent is on the Quai not far from Notre Dame and is fine but kind of pricey compared to some other choices. We paid almost as much as l'Initial for a lot less, but it was good. They specialize in rotisserie meats but also have the amazing Tour d'Argent quenelles which is why we went there. Alas our favorite Ile St. Louis place closed a few years ago.
Reserve a few days ahead for most and definitely a day ahead for any as places with plenty of room last minute have it for a reason.