Restaurant du Marché, 59 rue de Dantzig, 15th arrondissement (= district), close to Boulevard Lefebvre (south end of street), 01.45.33.23.72. Rich food from the Southwest of France: duck, goose liver, pâtés, etc. (goes well with Madiran wine from the same region). Moderate to expensive.
Le Copreau, 15 rue Copreau, 15th arrond., 01.43.06.83.35. Nouvelle cuisine. Delicate food, good service, quiet. Moderate to expensive.
Maison Blanche, somewhere in the 16th arrond. The original Maison Blanche ("White House") became famous in the 1980s when François Mitterrand, the President of France, made it one of his favorite places to eat. Apart from the fact that he is no longer considered a good reference point, this venue closed and Maison Blanche re-opened later in the 16th arrond., but I have not been there. Reviews, however, have been ecstatic. Expect it to be expensive.
Le Vaudeville, place de la Bourse (stock exchange square), 2nd arrond., 01.42.33.39.31. Brasserie, open late, seafood, artsy clientele.
Le Toit de Paris, top of the Montparnasse Tower, 14th arrond. The best view of Paris at night, because it's the only place from which one cannot see... the Montparnasse Tower, since you're in it! Large choice, no particular style, good service, somewhat expensive.
Aux Iles Marquises, 15 rue de la Gaîté , 14th arrond., 01.43.20.93.58, near Edgar-Quinet subway stop. A lot of seafood, but not exclusively (I remember a rabbit stew...), very good, elaborate desserts, expensive.
La Mamma, 46 rue Vavin (between Boulevard du Montparnasse and Boulevard Raspail), 6th arrond., near Montparnasse, 01.46.33.17.92 (but you don't need reservations unless you're a very large party. You may just have to wait a few minutes to be seated if it is a busy night). The best Italian pizza in Paris. Crowded on week-ends, noisy, but fun. Cheap, which in Paris means $30 per person.
L'Amanguier, three locations: 51 rue du Théâtre (15th arrondissement), 01.45.77.04.01; 43 avenue des Ternes (17th arrond.), 01.43.80.19.28; 110 rue de Richelieu (2nd arrond.), 01.42.96.37.79. Same nicely varied menu at all three places. Rather light and delicate food, pleasant atmosphere, good desserts and moderate prices. The catch? Often crowded, reservations are not always honored on time, and service can be on the frugal side.
Josselin is one of the best crêperies in Paris, located on rue du Montparnasse (not to be confused with boulevard du Montparnasse!) near the Montparnasse train station and métro (another convenient and far less confusing station is Edgar-Quinet).
Good brasserie: L'Arcade, on Boulevard Haussman, near Gare Saint-Lazare, one block west of the intersection where the Brummel department store is. Fast but very professional service, consistent food, moderate prices. Most waiters speak some English. I especially recommend the "bavette à l'échalotte."
Ma Bourgogne, at the northwest corner of Place des Vosges. Has outdoor seating under the arcades. Specialties from Burgundy (of course), and "andouillette," which is a sort of tripe sausage, typically eaten with French fries. It's much better than it sounds...
On rue Grégoire de Tours, near boulevard Saint-Germain (between Odéon and Mabillon), Le Grégory is fine, especially if they have confit de canard (duck roasted in its own fat).
Another place nearby where the confit de canard is excellent (but also the beef bourguignon) is Le Tiburce on rue du Dragon (one block west of rue de Rennes, near the Saint-Germain-des-Prés church and subway stop.
An ex-colleague of mine recommends the following place:Le Télégraphe, 41 rue de Lille, 7th arrond., phone 01.42.92.03.04. He describes it as "Very hip, wide open space. Light, somewhat Mediterranean fare. Many Beautiful People go to see what other Beautiful People are there, but the food is excellent and the price is not too high."