Area 1. Le Marais
walk / culture / shops / cafes – locals
Can start from anywhere but you can get off Metro République on top, and walk down to Ile Saint-Louis and finish at Notre Dame. It's a full area to visit and great streets cross each other. From République, go down Rue Charlot and get lost along Rue Vieille du Temple, etc.
Marché des Enfants Rouges – Grab a quick lunch in this no-chichi hip/local food court.
APC, Maje, Kooples, Sandro, etc.
Rue Vieille du Temple, Rue des Francs Bourgois, rue des Rosiers...
Area 3. Montmartre
walk / MONUMENT / cafes – locals & tourists
This used to be the artist quarters of the end of the 19th century (Toulouse Lautrec, etc.)
Start at Metro Blanche, walk up Rue Lepic (where Amelie the film was shot), turn right to rue des Abbesses up to the Metro Abbesses (art deco masterpiece). Walk north and get lost in the small streets, get the Place du Tertre (this Place is packed and touristy but worth seeing once), finish at Sacré Coeur, and go down the garden to arrive at Metro Anvers.
Le Très Particulier – Kind of a mini-adventure to get there (which is fun), but a real Parisian experience with a low-key bourgeois entrance with a buzzer, you walk in the dark and stumble on this pretty hotel and garden. The bar is at the back of the hotel. They do brunch too but it's more on the pricey side - you pay for the view and garden experience.
Les Cocottes – One of my favorite restaurants
Concept is only cooking in "Cocottes" and the Chef is Christian Constant who has a few Michelin-star restos on the street and opened a more laid-back version. Good quality food and cooking but in a more modern vibe.
MUST have "La fabuleuse tarte au chocolat de Christian Constant”.
No reservations (back then) but as long as you're there at 7-7:30 pm you shouldn't wait too long. (since French have dinner from 8 pm)
Area 6. From Louvres to Arc de Triomphe
Louvres Museum – tourists
Go if you dig old art from 18th century and earlier. Seeing it from outside is enough for me personally.
champs elysees and ARC DE TRIOMPHE
North-East of Paris. Seafood, great vibe.
North-West of Paris. Simple French comfort food (nothing fancy) but it's more about nice romantic vibe with a very Parisian cute back patio. Make sure you sit there and not inside which feels more normal.
South-East of Paris. I've never been but one of the happening places in the past years. It's a space on the Seine that has a restaurant, night club, yoga, concerts, workshops...