I wrote this two years ago for another place, but I keep pointing people to it, so I thought I’d cut’n’paste here for posterity. The original question was about a short break away. Oh, and apparently, Samaritaine is closed at the moment, so for rooftops do Montmartre and the Tour Montparnasse.
Things to do: avoid the places you’ll have to queue. Don’t bother with the Eiffel Tower, do the roof top cafe at the Samaritaine department store. Don’t do the Louvre — or at least, stick to the outside, the Jardins des Tuileries and the shopping centre under the glass pyramid. Also — a food hall is under there for cheap tasty international cuisine. For art, do the Musée d’Orsay instead.
Get a hotel in the Marais and do everything on foot — there’s loads of picturesque roads around there. See the Place des Vosges, walk as far as La Bastille and Place de la Concorde. Check out the bouqinistes, the river walkways along the Seine and Pont de L’art. Do the first few meters of the Bvd St Michel on the other side of the river — as far as the Deux Magots. There’s no real need to get on the metro or go further afield.
Bar-hop around the Marais for gay Paris life — Cafe Open on the corner of Rue St Croix de la Bretonnerie and the Rue des archives. The terrace in front of the Marronier, the, er, naughty upstairs at Quetzal si cela te branche.
Some things you can do for free: the Madeleine church inside and out, (check out how the front of the church is reflected in the front of the Assemblée Nationale on the other side of the Place de la Concorde) Samaritaine’s roof top, shopping but not buying in BHV, the walk along the Grands Boulevards with the mini arcs de triomphe, the doors with the lion carvings on the Rue vielle du temple (as featured in Dr Who City of Death), wandering around the Forum des Halles, and the outside of the Pompidou centre. Browse for haute couture in the Place Vendome. You used to be able to go around the Opera for free during the day, but I think they’ve stopped that now.
I spose these things will be old hat to you if you’ve been to Paris before… that’s when you need to get on the metro and go further afield to see some of parks a bit further out (Citroen, Buttes Caumont, Jardin du Luxembourg around the French upper house, the Sénat and the two either side of Line 1, Bois de Boulogne, Bois de Vincennes), or the Moulin Rouge or Montmartre or les Invalides, or the Rodin museum, or the Montparnasse, the highest tower block in the city, or the catacombes, or the sewer tour, or the walk from the bastille along the old canal, or the Champ de Mars, or BCBG of the 16th or the chinatown district in the north east or Père Lachaise cemetary (Oscar Wilde, Jim Morrison, very moving monuments to the Nazi death camps)
… gee, I wanna live in Paris again!
EDIT 2013 – see this amazing (French language) list of places to get good views over Paris.