As mentioned above, Le Marais (or Jewish quarter) and, of course, Montmartre, where you can see Le Moulin Rouge and the big church on top of the hill (it used to offer great city views, but now the trees block them).
Also, walk along the Seine, especially where Les bouquinistes (old book sellers) can be seen. L'ile de Saint Louis is a nice area, and so is Les Vosges (beautiful park, interesting neighborhood).
I would like to go to Paris and spend some good time there in the summer of 2015. Let's see how things are by then... Hopefully, by that time you'll be the one giving me pointers.
Ah! Before I forget, the Place de l'Hotel de Ville used to be a great spot for people watching. As for eateries... restaurants in Paris tend to be fairly reliable. If I were you, I'd try the ice cream in the Ile de St Louis (cannot recall the name) and eat patisseries daily. 🙂 They're really good!
I can second most of these suggestions (I'm not familiar with Place de l'Hotel de Ville). Let me add couple. Ile de la Cite is right over the bridge from Ile de Saint Louis. That is where Notre Dame Cathedral is. There are fun restaurants on both these islands. Autour de Notre Dame is an interesting restaurant right across from the cathedral. And across the bridge from Notre Dame to the left bank, if you scout around a bit you will find "Shakespeare and Company'" a famous bookstore with books in English and French.
On the right Bank, across from Ile de Saint Louis, within walking distance, is the monument that commemorates Bastille Day.
My wife and I enjoyed several museums, but none more than Musee l'Orangerie (hope I spelled that right). It is in the tuileries (I'm sure I got that one wrong), and is easily reachable by the Paris Metro. l'Orangerie has great impressionist paintings; and outside, at elast when we were there, the Rodin sculpture, "The Kiss." There is good view from there, too, with the Eiffel Tower in the background.
Avoid the Pomidou center. We didn't think it was worth it. And there are no Picassos in the Picasso museum. It's a collection of paintings he liked by other artists.
Another highlight for us was the Arc de Triomphe. You can go in it, and from the top, you can see all around: the Eiffel Tower, and you can look down the Champs Elysees. And I might suggest a walk down the Champs Elysees.
I will suggest not bothering with the Eiffel Tower, at least not when trying to make the most of a short visit. It's very crowded, with long lines to get in.
That's all I know about it!
