You are bound to stand in some lines so if you want a view of Paris from above I would suggest standing in line to walk up the towers of Notre Dame. You will be right in the center of Paris and still have a beautiful birds-eye view and be right next to the magnificant gargoyles. I hope you have read Hugo's "Hunchback of Notre Dame". After the towers you can grab a crepe across the street before you go into the magnificant cathedral, or visit the underground crypt of Notre Dame or the nearby Conciergerie.
Stroll the Bouquinistes along the Seine
I would never miss a visit to Pere Lachaise Cemetery. Pack a sandwich and a bottle of wine for lunch and enjoy dining with Colette, Moliere, Gertrude and Alice, Proust, and countless others
My favorite museum is The Carnavalet Museum, located in the Marais not far from Notre Dame. This free museum houses the history of Paris as well as being located in one of the most charming and historic areas of Paris.
Take the metro to stop Abbesses (an iconic Art Nouveau station entrance) and walk up the hills towards Montmartre and Sacre Coeur. This is quite touristy but the views are breathtaking and if you leave the area surrounding the basicila and Place de Tertre you can wander through some wonderfully historic streets. I do love this area of Paris.
I may be the only person in the world who would suggest skipping the Louvre, but then I've also spent countless hours there. Besides, the line to get in will waste half your day unless you have a museum pass. Go see the Louvre but stay outside and enjoy the surroundings.
That's a quick 3 days in Paris and you haven't even begun to scratch the many layers of this beautiful city or it's surrounding countryside. If you are going to take a day trip out of Paris I would suggest Veaux Le Vicomte rather than the overcrowded Versailles.
Please let me know if you would like me to blog about other things to do in Paris.