Help us find a district to rent an apartment in Paris.
 

We will be renting an apartment in Paris for the first time. We want to be a few blocks from a metro, near cafes and a market, in a relatively quiet area a night. We would very much appreciate any ideas you nay have.

You can find a property to meet those specifications in virtually any part of the city. Best bet for getting useful assistance here - provide description of traveling party, dates, budget, interests, any restrictions/preferences.

When considering a specific apartment, get as close to the actual street address as possible, do not go by "in the area of" or "near to" but the actual street. Then look it up on a map site like Google earth or maps street view.

Yes, except the central areas are not generally that quiet at night, although any one apt. could have a configuration that made it so. There are cafes anywhere, but you aren't going to have as many cafes in the outer arrondisements or quiet areas, at least not every few feet.

I think a lot of people like the 7th arrondisement for some of these reasons, that there are areas that are quiet but not too far away from metro or some cafes. I like the 13th-15th and bottom of the 5th for these reasons (although if you are near a main street, they can be noisy anywhere, and I just wish they'd outlaw motor scooters in Paris).

We stayed in this apartment on I'le Saint Louis: http://www.vrbo.com/360183
It was central, close to 3 metro lines and very, very quiet at night.

My husband and I stayed at this studio apartment:

http://www.vacationinparis.com/apts/id_180.htm

While the surrounding area was busy with shops, restaurants, and markets, this little street was quiet. It is close to the St. Michael metro, the batobus, and a short walk over to Ile de la Cite, where Sainte Chapelle and Notre Dame are. There isn't air conditioning, though.

Those criteria apply to just about anywhere, though the "quiet" crtierion could limit you to some parts of some arrondissements. It would be more helpful to know how much you want to spend.

We loved this apartment - quiet, close to cafes and metro. Delightful owners

http://lovely-paris-apartment-rental.com/home_b.html

I often stay in a friend's apartment not far from the one SusannahT recommends, and as far as the area goes, I second the recommendation. It's a little out of the main tourist centres (but all the better for that, in my view), but close to public transport, and to the Marché Aligre; I notice more hotels in recent years, but for the moment this is a part of Paris where ordinary Parisians are living their regular lives, rather than being in a touristic bubble.

You say renting for the first time--is it your first time to Paris? I would guess so, since you would probably have a much better idea of where you would like to stay.
As has been said, you can find your criteria in many areas. Do you require an elevator? Do you have all your sightseeing and restaurants in mind/planned or do you think you'll need advice from a desk/concierge along the way of your trip. How long do you want to stay in the apartment? Have you looked at any of the myriad sites that rent apartments for an idea?