While just a day in Paris isn't enough, it's better than a day anywhere else. Here's how to see as much as possible in 24 hours.
Get high
To see as much of the city in as little time get to one of the city's highest points. The best three in Paris are
The first two will cost you and involve waiting in line. Sacré-Cœur is free (at least the front steps are; the dome will set you back €5) and there's no wait, but the hike to the top of Montmartre takes time and energy.
Get low
Take a boat trip down the Seine (ideally at night) to see many of Paris's major attractions at eye level. Yes, it's touristy. But a Parisian friend of mine recommended it, which gives it street cred.
Uncle Rick Steves recommends these three companies:
Stroll through The Marais, a center for Paris's gay and Jewish communities (it must be Mecca for Barney Frank). Absorb French culture by having a good sit in a sidewalk cafe. And check out La Bellle Hortense, which the new York Times describes as a "cozy Old World-style wine bar,[where] a straight and gay, leather-bound and tweed-wrapped crowd swirls wines by the glass and chats animatedly about highfalutin topics." Hea-ven!
Other neighborhoods worthy of a stroll: