Places of interest in the 9th & 18th arrondissements:
Musée Gustave Moreau (14 rue de La Rochefoucault, Me Trinité)
Musée de la Vie Romantique (16 rue Chaptal, Me St George, Blanche ou Place Pigalle)
Musée Jacquemart André (corner rue de Téhéran & 158 blvd Haussmann)
Passage des Panoramas (at Blvd Montmartre and rue St Marc)
Nadia & Lili Boulanger Conservatory of Music & Dance (rue de Douai, across from Lycée Jules Ferry)
Le Montmartre de Toulouse Lautrec (coffee shops and bistrots Le Chat Noir, Le Mirliton)
Musée Dali (11, rue Poulbot, Me Abbesses)
Musée de Montmartre (12, rue Cortot, Me Lamarck-Caulaincourt)
Montmartre Cemetery (20 Avenue Rachel, Me PlaceClichy): Composers Hector Berlioz, Jacques Offenbach, dancer Nijinsky, film maker François Truffaut and painter Degas are buried in the Montmartre Cemetery. It may seem also hard to imagine DEGAS moved 8 times in his life within a 10 block radius from his birth place. Degas spent the last 5 years of his life at 6 boulevard de Clichy.
Musée de l'Opéra (Pl. de l'Opéra)
Musée Grévin (10 blvd Montmartre)

Places of interest on the Right Bank:
Galerie "Arcade" Vivienne ( rue Vivienne et rue des Petits Champs, 2e arr.)
Passage du Caire ( Me: Sentier, 2e arr.)
Passage Jouffroy (Me. Richelieu-Drouot, 9e arr.)
Passages des Panoramas (Me: Bourse, 2e arr.)

Green spaces:

There are 10 acres of green parks in the 9th arrondissement of which, the parc d'Anvers, Montholon, Estienne d'Orves, Alex Biscarre and Square Berlioz (see below) were the main ones; not to mention the gardens of the Museum of Romantic Life.

vintimille.jpg (55163 bytes)
Edouard Vuillard, Place Vintimille, 1911, five-panel screen, distemper on paper laid down on canvas, National Gallery of Art, Washington.  Place Vintimille was Place Adolphe-Max, Square Berlioz 's old name. Vintimille came from a Napoleonic battle.
See: http://www.nga.gov/feature/artnation/vuillard/index.htm

vintimilleblackwhite.jpg (37616 bytes)
Place Vintimille, 1910-1912, photograph by Edouard Vuillard
Note: The flat to rent is on 4th floor!

Churches:
Eglise de la Sainte Trinité (3 rue de la Trinité)
Eglise Notre Dame de Lorette
Eglise St Eugène
Eglise Luthérienne de la Rédemption
Grand Synagogue de la rue de la Victoire

Other:
Notre-Dame-de-PARIS (Ile de la Cité, bus #74) has free public concerts on Sunday afternoons.

Art Auction Houses:
Hôtel des Ventes Drouot (9, rue de Drouot, 9e, bus #74 from Place de Clichy to Drouot-Provence stop)
Sotheby's (76, rue du Fg St Honoré, 8e)
Christie's (6, rue Paul Baudry, 8e)

Flea markets:
 Between the Porte de Clignancourt & Porte St Ouen (Metro station: Pte de Clignancourt): Marché Biron or Vernaison are the upscale antiques markets.(Sat-Sun-Mon).

Links:

Paris website : Paris website
ParisFashionable Right Bank: Fashionable Parisians Doing the Right Thing
[SanFrancisco Chronicle January 28, 2001]

Good Eats/--Où dîner ce soir?

http://www.EatinParis.com  (by district, quite helpful)
http://www.Reservethebest.com  (comme ci, comme ça)
http://www.zagat.com  (a well known quantity)
http://www.Bparis.com  (for France fanatics)
http://www.patriciawells.com  (too much self-promoting)

Bibliography:

The Spirit of Montmartre: Cabarets, Humor and theAvant-Garde (1875-1905) by
Philipp Dennis Cate & Mary Shaw ( JaneVoohees, Zimmerli Art Museum Rutgers,
The State University New Brunswick, NewJersey, 1996).

The Banquet Years: the origins of the Avant-Garde inFrance (1885 to World War
I) by Roger Shattuck (Vintage Books, revisededition 1968).

Montmartre du Plaisir et du Crime par LouisChevalier (Editions Robert
Laffont, 1980).

Transforming Paris: the Life & Labors of BaronHaussmann by David. P. Jordan,
University of Chicago Press, 1995.

The World of the Paris Café: Sociability among theFrench Working Class
1789-1914 by W. Scott Haine (John HopkinsUniversity Press, 1996).