Nearby you find Brasserie Lipp, a bit more touristy but an institution nonetheless, worth a visit. If you're looking for somewhere more upscale go to Ralphs for lunch, the burgers are delicious and their patio the cutest thing ever. Another option is La Société for dinner: after all these years it still got it.
In the evening head to Bastille for dinner at Chez Paul, a very French restaurant where every dish is delicious. I love their confit de canard so I always go for this one.
I adore the 8eme. If you're in the area go visit the Jacquemart-Andre museum, the French version of the Wallace Collection in London or the Frick in New York. A gorgeous location and as we are in France, great restaurant too. You can start the day with a brunch there before checking out the exhibits. After that you can go for a walk at the beautiful Parc Monceau and visit the neighborhood. For dinner there's Les Gourmets des Ternes an authentic French restaurant loved by the locals and artists (you can see their pictures with the owner on the walls, like a French version of Ciro Pomodoro in London). I saw Charlotte Gainsbourg there once.
The other option for Sunday evening is to walk around Montparnasse, where the trains from Britanny (the galettes/Crepes region) arrive hence the many Crêperie there. The one I love is La Crêperie Josselin but you can choose any around the station and you cannot go wrong.
Monday morning it's time to go back to London and start the week with a detox program :)
Bistrot Viviene - 4 Rue des Petits Champs, 75002
Le Pas Sage - 1 Passage du Grand Cerf, 75002
Le Compas - 62 Rue Montorgueil, 75002
La Mano - 10 Rue Papillon, 75009
Little Apple - 27 Rue de Saintonge, 75003 Paris-3E-Arrondissement
Les Philosophes - 28 Rue Vieille du Temple, 75004
Au Petit Fer à Cheval - 30 Rue Vieille du Temple, 75004
La Palette - 43 Rue de Seine, 75006
Galerie Rauchfeld - 22 Rue de Seine, 75006
Brasserie Lipp - 151 Boulevard Saint-Germain, 75006
Ralph's - 173 Boulevard Saint-Germain, 75006
La Societe - 4 Place Saint-Germain des Prés, 75006
Chez Paul - 13 Rue de Charonne 75011
Jacquemart-Andre Museum - 158 Boulevard Haussmann, 75008
Les Gourmets des Ternes - 87 Boulevard de Courcelles, 75008
La Creperie de Josselin - 67 Rue du Montparnasse, 75014