Roam around Marais, the 11th and the surrounding areas. These are the most hip neighborhoods in Paris, which have a very local-oriented lifestyle (boutiques with handmade stuff and trinkets, local coffee shops, bars, delis and restaurants where you can easily make friends including the staff). Lots of authentic food from around the globe.
+ Jewish and Chinese districts (Marais), Muslim (Belleville, the 11th)
Some of my faves: Pili Pili, Au Petit Garage, Le Chat Noir, Orange Mecanique and their neighbors (Rue Jean-Pierre Timbaud and Rue Oberkampf), Le Progres, L'etincelle (bar), L'etoile Berbere, Nour (Middle-Eastern food), Babka Zana (bakery), Aleph (patisserie + rose/orange blossom/pistachio lattes!), Da Vito/Moonshiner (Pizza/Speakeasy), L'epicier (Middle Eastern-style speakeasy), Gem la Patisserie (Southeast Asian macarons, which unlike Laduree are freshly made every day)
P.S. La Gare is a bit far, but it's the best jazz club in Paris.