Dance

Opéra National de Paris

The Paris Opera is the primary opera company of France. It was founded in 1669 by Louis XIV as the Académie d'Opéra. 
Classical ballet as we know it today arose within the Paris Opera as the Paris Opera Ballet and has remained an integral and important part of the company. 

Currently called the Opéra National de Paris, it mainly produces operas at its modern 2700-seat theatre Opera Bastille which opened in 1989, and ballets and some classical operas at the older 1970-seat Palais Garnier, which opened in 1875.

Each year, the Opéra presents about 380 performances of opera, ballet and other concerts, to a total audience of about 800,000 people.
Bastille

Opéra Bastille
Address: Place de la Bastille 75012 Paris
Access: Tube Bastille / Bus: 20, 29, 65, 69, 76, 86, 87, 91 / RER: Gare de Lyon

Opéra Garnier
Address: Place de l'Opéra 75009 Paris
Access: Tube Opéra
Phone: 08.92.89.90.90 or 01.71.25.24.23 (from abroad)
More info here.

Théatre du Châtelet

Opened in 1826, the Théâtre du Châtelet is located at Châtelet in the 1st arrondissement of Paris. They primarily stage operas and classical concerts and, since 2002, have played host to the Césars cinema award ceremony. The magnificent fresco in the bar-foyer of the theatre was created by Valerio Adami.
Address: 2 rue Edouard Colonne 75001 Paris
Access: Tube Châtelet, Cité, Hôtel de Ville / RER: Châtelet - Les Halles

More info here

Théatre de la Ville

The Théâtre de la Ville (meaning the City Theatre) is one of the 2 theatres built in the 19th century by Baron Haussmann at Place du Chatelet, Paris, the other being the Théatre du Chatelet. It is located at 2, place du Châtelet in the 4th arrondissement. Included among its many previous names are Théâtre Lyrique, Théâtre des Nations, and Théâtre Sarah-Bernhardt.
Address: 2 place du Châtelet 75004 Paris
Access: tube Châtelet / Bus: 21, 38, 47, 58, 67, 69, 70, 72, 74, 75, 76, 81, 85, 96 / RER: Châtelet - Les Halles
Phone: +33 (0) 1 48 87 54 42

More info here.

Théâtre National de Chaillot

Situated at Place du Tocadéro in the 16th arrondissement, the Théâtre National de Chaillot is one of the most prestigious venues in the capital.
It is known not only for the role it played in the history of live shows since the creation of the Théâtre National Populaire de Jean Villar (which has seen some of the first performances of the biggest stars of the last 50 years) but also for its role in the history of France, since it was at the Théâtre National de Chaillot that the Universal Declaration of Human Rights was signed on 10 December 1948.

Its 3 rooms can accommodate more than a 1000 people every evening and the Grand Foyer opens onto the fountains at Trocadéro, the Eiffel Tower and the Champ de Mars, offering one of the most famous views in the world both day and night.

Address: 1 place du Trocadéro  75116 Paris
Access: Tube Trocadéro / Bus: 22-30-32-63-72-82 / Train: Gare Saint-Lazare
Phone: +33 (0) 1 53 65 30 00

More info here