Which neighborhood in Paris?

Le Marais is where the mansions of the pre-revolutionary French aristocracy along with the oldest building in Paris are all located. (51 Rue de Montmorency was built in 1407). The district is like an open-air museum for architecture.
You might enjoy the area in the 5th arrondissement near Luxembourg Gardens. With any luck on your dates of travel, there may be rooms available at the Hotel Les Dames du Pantheon, Hotel des Grandes Ecoles or the Hotel Observatoire Luxembourg.
Have fun in Paris!

I don’t know about all your criteria, but I enjoyed the area around the Place d’Italie in the 13th

We were just in Paris and explored the La Butte aux Cailles area which is near the area @stephen mentioned. Maybe a little closer to Covisart. It’s the old Communist area of Paris with little Haussmann penetration so it has small houses and little neighborhood blocks and super modern places as well. We went for the street art that decorates the area and to explore.

In that neighborhood it doesn’t feel like you’re “in Paris” but the metro is right there. That being said I have no idea what the short term stay situation is.

Honestly I admire your determination to explore but with a day+ there’s something to be said for staying in an area you’re familiar with when time is short.

Have great trip,
-Tod

Some areas that have similar charm to the Marais are the 5th and 6th arrondissements. I do second the recommendation for the 13th, however more so on its border with the 5th. The base of the rue Mouffetard next to the Église Saint Médard , for example, is very lovely. The latter is very close to both the Jardins des Plants, the Luxembourg gardens and the mosquée of Paris. The areas around Notre-Dame-des-Champs and Saint Sulpice is also very nice. In both, you will be a stone's throw away from the Luxembourg. The streets directly between Saint Sulpice and the Luxembourg are particularly "Sleepy", despite being located in one of the most desirable locations in Paris.

Everyone loves the Marais. I'll have to stay there sometime. We always stay in the 6th or 7th. Something about the Left Bank seems quieter to me, notwithstanding the tourist behemoths of the Eiffel Tower and Invalides. Champ de Mars is a nice park with the money-shot view. But based on your criteria I think the 6th is more up your alley, around Jardin Luxembourg. Fantastic park, lots of cafes, several markets.

Honestly I admire your determination to explore but with a day+ there’s something to be said for staying in an area you’re familiar with when time is short.

Ditto...and on this upcoming trip, maybe visit one of the neighborhoods suggested here for future consideration,

Personally, I would not want to stay in the Marais...it is very crowded with tourists (and locals), streets and sidewalks are narrow, crowded...not my cup of tea. But if you like it, I say go there again.

I stay at a hotel in an un-touristy area in the 15th, very French, easy Metro access, tons of great places to eat. Discovered this area a decade ago, and have stayed there ever since (we go to Paris once, sometimes twice a year).