My advice to anyone going to Paris, based on my favorite memories (clearly, lots of my memories are food related):
Go to mass at Notre Dame
Give some spare change to a Metro musician.
Recreate famous works of art for photographs. The guards at the Louvre will laugh at you, but really, they're probably kind of bored anyway.
Watch an organized protest. They're surprisingly easy to find.
(For the bibliophiles) Go to Shakespeare and Company. Find a likely looking book, sit, and read for hours. Or maybe play the random piano on the top floor of the store.
Eat hot pain au chocolate from the boulangerie around the corner from the institute building.
Even if your French isn't very good, go to a play. It's amazing how much you'll understand.
Have your mind boggled by the modern architecture and sculpture at La Defense. Do a thumbs up in front of Le Pouce.
Eat gelato at Amorino.
Go to Saint Chapelle, sit down, and watch the changing light come through the stained glass.
Wear all black at least once (especially if it's winter).
Eat lamb, duck, rabbit, and escargot. You won't regret it.
Play tag on the metro.
Eat at Breakfast in America if you miss ranch dressing or American mustard as much as I did, but ONLY if you're in Paris for more than six weeks!
Window shop on the Rue de la Paix and pretend that you have the money to buy Mikimoto pearls or this necklace.
Go to the Musée D'Orsay and the Musée de l'Orangerie, my two favorite art museums. Also visit Monet's house and gardens at Giverny, then tell me about it, since I never got a chance to go.
Have a kebab (pronounced "kay-bob," not "kuh-bob") and frites for lunch. Then have a nutella crêpe.
Buy lots and lots of scarves. I brought four back for one of my friends alone.
Go to Père Lachaise Cemetery. This might seem like a weird tourist location, but you'll be amazed to see whose graves you can find. Make sure you pack in some lipstick so that you can kiss Oscar Wilde's grave.
Visit the Eiffel Tower in the evening. Ride to the top at sunset, then get down in time to see it sparkle on the hour.
There are so many more, but these are a few of my favorites! Paris, tu me manques.