What to do in Paris for 3 days?

1) Eiffel Tower. Then Metro to Notre Dame. Explore on foot — latin quarter to Marais/Pompidou Centre passing through the Louvre. Return for dinner/bars/nightife every evening
2) Louvre Museum + Other museums (Picasso/Orsay etc)
3) Sacre Coeur down to Arc De Triomphe. Explore the Seine — picnic/wine around there maybe and plan when you'll return…

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1 Day Champ'elysee,art de triump,layfette
1 Day Louve Musuem and Palace
1 Day Eiffel Tower, Siene River Cruise
3 full day is sufficient

Night time river boat trip on seine

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My favorite places:
1) Eiffel Tower is a must — maybe combine with a ship tour on Saine.
2) Churches: Best: No1 Saint Chapelle (near to Notre Dame) No2. Sacre Coer No3. Notre Dame (i like the others more)
3) The Quarter in Monmatre (near Sacre Coer)
4) Louvre ( it's a must) but the «Centre Georges Pompidou» is more modern art and i liked it more.
…

don't plan, relax and enjoy the cafes and food

If you're really into history and/or art I would reserve one day just for Louvre.If you like skyscrappers and modern architecture you might want to take a short visit into the La Defense hood.
Also, a small advice: don't go on the top of the Eiffel Tower, instead go for the top of the Montparnasse Tower. It's taller and you can see the whole of Paris, Eiffel included. :)

1) Montparnasse, Eiffel Tower, Arc de Triomphe, Champs-Élysées, Louvre — Tuileries, Châtelet–Les Halles, Place de la Bastille, Tomb of Jim Morrison, on foot
2) Versailles, Forêt domaniale de Fausses-Reposes, Château de Ville-d'Avray, National Estate of Saint-Cloud, possibly on bicycle.
3) Louvre Museum, and if there is time,Catacombs of Paris