I think for a first timer it's still great to see all the world famous sights, like the Eiffel Tower, the Arc de Triomphe, the Champs-Elysees, Sacre-Coeur, Notre Dame and the Louvre.
I've been in Paris at least 10 times and have not seen anything so far (still missing Musée d' Orsay or the Parthenon for example).
But my two last visits brought me for example to this (less visited) places:
Montparnasse Tower (view platform on top of a high riser, but with the advantage to see the Eiffel Tower from there, and it has far fewer visitors and therefore almost no waiting time)
Jardin de Luxembourg (a nice park)
the cemetary of Pére Lachaise (with lot's of famous people, burried there Victor Hugo, Jim Morrison from the Doors and many more; head for a map to the flower shop opposite the main entrance)
Parc de Buttes-Chaumont, another nice and quite suprising park (and somehow famous for beeing a poster on the wall in one of the appartements in the sitcom "Friends")
and finally
the Cathedrale of Saint-Denis, where many of the old French kings who came after Charlemange are burried