My "can't-leave-Paris-without" list

Les Nymphaes in the Musee de l'Orangerie, © 2012, Joan Klau

• Musee de l'Orangerie houses Monet's waterlily series as they were designed to be displayed - in 2 big oval rooms, with 4 paintings per room. What's most incredible is how sunlight from the skylights of this old greenhouse influence the colors of the paintings. If a cloud passes over, it completely changes how you view the paintings. Amazing. Everytime I go to Paris, I easily spend an hour or two in just those two rooms.  It is one of my happy places.  The basement has non-Monet stuff worth visiting if you have time.  More about why I love it here.
• Even if you aren't a museum person, the design of the Musee d'Orsay is pretty cool - the inside of an old railway station. But, if you do like art, it has a great collection of Impressionist art. 
• The amazing stained glass windows in Sainte Chappelle are best lit by morning light.  They're in the processing of cleaning and restoring the stained glass at Ste Chappelle, and it's quite amazing to see the difference between clean and dirty.  Just a tip: you can't really see the church from the street - it's tucked behind the wall around La Concergie so just south of the ornate black and gold gates that show off the French supreme court, look for a line forming and going into an arch on the west side of the street.
• A block away is Notre Dame, which you could easily spend an hour inside and out.  If you want to tour it, I recommend going first thing in the morning:  get in line for the tower stairs to see the gargoyles about 15-20 minutes before they open - that'll be the shortest wait all day.  Then tour the inside (I found the audio tour worth it).  Outside, don't forget to walk around the south side and eastern back end to appreciate the famous flying buttresses.  For the prettiest pictures, come back at sunset - in fact, I highly recommend that once you're done snapping shots of sunset's glow on the front facade, walk around the back and over the bridge to Île Saint-Louis and toast sunset with a glass of champagne at one of the cafes facing Notre Dame.
• My favorite Paris stroll is from Notre Dame to the Tuileries, detailed here. 
• I also love to stay in and wander around the Marais.  My favorite long lazy walk through the Marias is mapped out here.
• I love to make a pilgrimage to Montmartre for interesting sights (church, carousel, park), amazing city views, and a nice walk through an interesting neighborhood – all detailed here. If you're a fan of the movie Amelie, this was her neighborhood.  
• La Maison Angelina has the best hot chocolate (called l'africain), a pretty wonderful nicoise salad, and some insane pastries. #226 Rue de Rivoli, across the street from the Tuileries.
  
• Le Petit Zinc is a romantic art deco brasserie throwback to Paris 1920; service is great without being obsequious; and every last bite was delicious. The Fruits de Mer plats are hay-uge. It's right around the corner from Cafe de Flore and Les Deux Magots, 2 classic Parisian cafes - all of which are right at the St Germain des Pres metro. 

You'll find more favorite wanderings here.