Favorite local bistros, etc in 2nd Arron or nearby area
Le Mellifère, 8, Rue Monsigny, 2nd arr., comes to my mind and of course Chez Georges, 1, Rue du Mail (slightly overrun though).
In the 1st, you'd have L'Ardoise, Rue Mont-Thabor (usually some tourists, too).
Also, check out Place du Marché Saint-Honoré where you'll have some other places away from traffic noise.
Depends a bit at what end of the 2nd you are.
In the first highly recommend Point Bar, run by daughter of three star Michelin restaurant in Tours(Jean Bardet) and her father's influence is inherent in the food. Also Casaluna. In the second; more formal, expensive restaurants with high quality food and service are Le Versance and Drouant.
OK, revealing one of my little secrets here. ;o)
Café de l'Epoque, 2, Rue du Bouloi, 1st arr. Right at the one end of the wonderful covered passage Vérot Dodat close to the Palais Royal/Banque de France/Bourse. Don't miss the hip By Terry shop right next door. It's a small brasserie/bistrot rather than a café. Always packed, especially at lunch. Few tourists. Daily changing specials. You can also just stand at the zinc (counter) for a glass of wine and a sandwich.