-- Avenue de l'Opéra, Quartier Montorgueil, Richelieu library, Gallerie Vivienne, Passage Choiseuil, "Japan town", Bourse --
The 2nd arrondissement is "second only" to the 1st, shall we say--in terms of its central location and quick access to everything. The Palais Royal is officially in the 1st, but it borders the 2nd. Rue Montorgueil starts off in the 1st, but is mostly in the 2nd. Les Halles also sits at the border between the two.
As for the Opéra Garnier (best viewed from the 2nd), it is technically in the 9th.
Historically a garment district, the 2nd has become, over the past twenty years, one of the most vibrant and trendy neighborhoods, in particular for shopping and eating. The vortex of this transformation is a vast pedestrian zone between rue Etienne Marcel and rue Réaumur , englobing rue Montorgueil, rue Montmartre, rue Mandar, rue Tiquetonne, rue Bachaumont, rue Marie Stuart, rue Saint-Denis, rue Greneta, rue Dussoubs, and rue Saint-Sauveur (nearly exhaustive). This is one of the 'hoods that'll keep you in sync with the times. Not a month goes by without some new concept popping up.
Living in the 2nd is boon, but also a "bust your butt" proposition, given the difficulty of finding a suitable apartment there, and given the speed at which everything seems to scurry. The best offers are snapped up quickly. Many spaces will require imaginative and costly renovations to make good of cramped spaces or transform old garment factories into lofts.
Perhaps the best Japanese "home-style" cuisine outside of Japan can be found in the 2nd, boasting a host of ramen and soba eateries (not all of equal worth, of course). Densely packed into the area between the Avenue de l'Opéra, rue des Petits-Champs, and rue du 4 Septembre, they surround three notable sites well worth your visit.
The Square Louvois is something of a secret--the only green space in the entire district--tiny though it may be. It features a magnificent fountain representing the four great rivers of France.
Just across the street is the recently renovated Richelieu National Library, boasting a remarkable reading room, open to the public.
The "Bourse" refers to the neo-classical building previously home to the stock exchange, now an events venue also called the Palais Brogniart.
Take a spin around the Place des Victoires, remarkable for its elegant rotund architecture (more than for the statue of the horseman).
The "secret" side of the 2nd is revealed by its numerous passages, or glass-covered walkways, also called "galleries". These are the 19th-century version of the 20th-century shopping malls. Fortunately, they remain charming and replete with curiosities. Not a single brand store to be found. Among the best-known are the Gallerie Vivienne, le Passage Choiseuil, le Passage du Grand-Cerf, and the Passage des Panoramas.