Which Paris arrondisement? Fun neighborhood, but not too touristy

14th around Edgar Quinet, Vavin metro stops. We love this area. Easy walk through Luxembourg Gardens to center, lots of cafes including the best crepe street (Rue Montparnase) and the great brasserie (Coupole, Rotonde etc) Plenty of bakeries, grocery stores as well as cafes and such. Not particularly touristy.

The area Janet suggests is a good choice. Also consider the 3d, the northern part of the Marais. And the 11th, east of Bastille. I haven't stayed in the area around Place des Nations, but I liked its looks and Metro/RER connections.

We haven't stayed in the 14th (and it does sound enticing!) but we enjoyed our stay in the 13th (Butte aux Cailles: Knoll of Quails) very much. Someone wrote: "Its slight rise meant that it kept its character as modern Paris spread, and it entered the 20th century as a blue-collar enclave of row houses. Those modest houses are still there, wrapped with vines and flowers, and distinctively human-scaled amid the concrete and glass postwar tower blocks that grew up around them. Today the area... has become kind of a hip refuge... known, among other things, for its restaurants... It's the classic traveler's vanity to try not to feel like a tourist, to have 'your' neighborhood, and this apartment was feeding that weakness in the best possible way." If you have more than a week in Paris, you might do what we did and stay in apartments in two different neighborhoods for a week each. In addition to experiencing two arrondisements, we didn't have to worry about how to dry huge bedsheets in a tiny apartment!

Since you've seen all the major sites, I would pick the 10th Arrondisement by the Canal St. Martin. We were there in 2015 and it was our third time in Paris and the first time that I actually enjoyed myself. The neighborhood is loaded with good restaurants - just not ones that are known to all the tourists. I guess the major tourist site is the Pere LaChaise cemetery, which is well worth an afternoon. We had a great dinner at Le Petit Cambodge, which was one of the targets of the terrorist attacks. I intend to return to the 10th Arr. and enjoy another meal there.

We stayed at the Le Citizen Hotel and just loved it.

It is not in a single arrondissement or neighborhood but I like the area formed by Rue Saint Antoine/Rue Faubourg Saint Antoine, Rue de Turenne/Rue Beranger, Rue du Temple, Avenue de la Republique and Blvd Voltaire. I have stayed in the 14th near Edgar Quinet metro station and in the 13th near Corvisart metro station and I agree that those areas meet your request quite well. I think that they are quieter than the area that I suggest. Another area that might work for you is the St Georges quartier of the 9th arrondissement. When I was looking to purchase an apartment in Paris, the St Georges quartier and the Buttes aux Cailles were initially my two top areas but instead I bought near Bastille metro station. I found all three areas to have good transit connections with the 13th being the least but not bad by any means and none of them felt super touristy.

The 10eme, 11eme and 12eme arrondissements would be my choice. There is an awful lot to do here, but they are still working class neighborhoods.
The 13eme and 14eme are not tourist-ridden, but it's not very convenient for walking around. There isn't much to do here but go to the movies.
If you are looking to rent an apartment, you won't find many available in the 13eme and 14eme.

I like JHK's suggestion, followed by Chexbres. This is if you want to be in an area with lots of good restaurants, cafés, shops, excellent transit links etc. As I'm reading it, JHK's suggestion equates to parts of the 3rd and 11th arrondissements.

The Butte aux Cailles neighborhood is also very charming, but a bit further out.