Place de la Concorde -- This is where Marie Antoinette and Louis XVI were beheaded. Now it's a large square filled with fountains and an Egyptian obelisk. From here you can see the Eiffel Tower, Hôtel des Invalides, the Champs-Élysées, The Arc de Triomphe, and La Madeleine. More on those later. We visited this place several times to see the sites in various shades of night and day.
Le Marais & Châtelet-Les Halles -- This is one of my favorite parts of Paris. Eat falafels in the Jewish Quarter, watch street performers by Centre Georges Pompidou. Lots of pastries in this area (along with most other areas): pains au chocolat, réligieuses, baguettes, and crêpes.
Hôtel des Invalides -- home of Napoleon's tomb and a military museum.
Rodin Museum -- Balzac, The Thinker and a bunch of other naked statues.
Musée d'Orsay -- Everything from Impressionism on: van Gogh, Monet, Degas, Toulouse-Lautrec, Manet, Renoir, Rodin, Whistler, etc. My favorite is Cain by a lesser-known artist.
The Louvre -- Everything from Impressionism back: da Vinci's Mona Lisa, Michelangelo's Slave, Venus de Milo, Egyptian artifacts, etc.
Arc de Triomphe -- climbed 400 stairs to the top for a great view of the city.
Eiffel Tower -- took a Bâteau Mouche (boat on the Seine River) tour from here, spent some time in the park, bought overpriced bottled water, took lots of pictures, didn't go to the top.
Champs-Élysées -- the big road that connects Place de la Concorde to the Arc de Triomphe. We walked down this a couple of times to do some people-watching and to visit the Virgin Megastore.
Victor Hugo's home -- pretty boring tour, but cool to have been there.
Basilique du Sacre Coeur -- large white church on the top of a hill.
Montmartre -- near Sacre Coeur are a bunch of Bohemian sites: Picasso's studio, van Gogh's apartment, hangouts of famous poets and authors, Place du Tertre where all the aspiring artists (con and otherwise) congregate. Down the hill is the Pigalle area, home to the Moulin Rouge and tons of good music shops.
Versailles -- Palace of the Sun King, Louis XIV, crowned and married at the age of four. We went on the tour of the gardens on a Sunday afternoon, the only time they run the immense (and expensive to operate) system of fountains, accompanied by Baroque music. We also toured the Palace. The Versailles Treaty was signed in the Hall of Mirrors, ending the First World War.
Sainte-Chapelle -- Wendy's second favorite. Incredible stained glass windows that tell the history of the world from Genesis to the Second Coming with the life of Christ in the center. Moses is depicted with horns because of a mistranslation of the Bible in medieval times.
Cathédrale de Notre Dame -- took 200 years to build. Tried to go to the top, but the line was too long. After the gargoyles up top, my favorite feature is the depiction over the center door of the Final Judgment with Christ in the center, devils taking people off to His left, and angels taking others off to His right.
Catacombs -- bunches of bones unearthed from Parisian cemeteries and arranged by monks in underground tunnels. Ours was the quickest tour on record, with Wendy pulling me through the tunnel maze as quickly as she could run.
Pere Lachaise Cemetery -- This was right by our hotel. Its claim to fame is (much to the dismay of the French) the grave of Jim Morrison (of The Doors), which can easily be found by following the graffiti. Among the others buried here are Frederic Chopin and Oscar Wilde.