Follow the itinerary for One Day in Paris: Arc de Triomphe, Avenue des Champs-Élysées, Rue du Faubourg St-Honoré, Palais d l'Élysée, Place de la Concorde, Jardin des Tuileries, Musée du Louvre, Île de la Cité, Cathédrale de Notre-Dame, Place St-Michel, the back streets of the Left Bank (Quartier Latin) and, if you choose, a cruise on the River Seine, followed by a very good dinner in a simple bistro or elegant restaurant.
Go to the Ile de la Cité to visit the Towers of Notre-Dame, then to the nearby Palais de Justice to admire the splendid Sainte Chapelle and the gloomy Conciergerie, then explore the Latin Quarter and the Invalides before taking the Métro to the Trocadéro station for a walk downhill to the Eiffel Tower and Champ-de-Mars.
If you haven't yet taken a cruise on the River Seine, that would be a good way to end the afternoon, or—especially—the evening. More...
In the morning, go to Montmartre to see the Basilique du Sacré-Coeur and the artist-filled Place du Tertre.
In the afternoon, choose a few more of Paris' excellent museums for visits. There are dozens. The one(s) you choose can be dictated by your own tastes, but I'd recommend the Musée d'Orsay, the Carnavalet (the museum of the history of Paris) and, depending upon the exhibitions, the displays in the Centre Pompidou or the Grand Palais.
If you have time left, spend it people-watching in Parisian cafés, and in nice restaurants at dinnertime.
Take a morning or afternoon stroll through Le Marais, once a swamp, historically Paris's Jewish quarter, but today also a trendy, lively arts and crafts neighborhood.
Spend some time in the many lovely Paris parks and gardens, (start with the Jardin du Luxembourg) and explore some of the medieval monuments such as the Église St-Germain-des-Prés and the Musée de Cluny.
Make a day-trip excursion to visit Louis XIV's splendid Château de Versailles, only a short ride from Paris by Paris airport.
A few more days? See our itinerary for A Week in Paris.