Neighborhood in Paris?

Just about every neighborhood in Paris is nice restaurants and if by markets you mean the weekly outdoor markets, there is a market in every arrondissement. You might like the area near the Rue Montorgeuil market street or the area near the Rue Mouffetard market street. I happen to love the 9th arrondissement, although some find it a bit too far away from the major tourist sights, and Rue des Martyrs is a great street leading to the 18th. If you are willing to be a little further out of the center, you can look around Rue Daguerre in the 14th. That being said, here is a link to an airbnb description of various neighborhoods in Paris that you may find helpful: https://www.airbnb.com/locations/paris.

Prior to our first trip to Paris I read someone's recommendation that a first-timer should stay "as close to the river and as close to Notre Dame as possible." I took that advice and booked an apartment in the Marais - for one week. Then we moved to the 13th for our second week to have a different experience and so we wouldn't have to wash sheets and try to find a way to hang them up! (Talk about lazy!) But we enjoyed being in a more "real" neighborhood our second week, and by then we had learned our way around the transportation and so forth.

Popular areas for American travelers seem to be:
Isle St. Louis (1st district or arrondissement)
Rue Cler (7th)
Marais (3rd & 4th)
Luxembourg/St. Germaine-de-Pres (mostly 6th)

You say you want to be close in to nice markets, etc, so you'll probably want to avoid double digit arrondissement.

Hello Amy,
We always rent the same apartment in Paris. The owner has two different sized apartments. I can speak of the larger one located in the most perfect spot in the Marais. It is just steps from the metro yet it is very quiet. A grocery store and many cafe's are located within an easy walk. The famous Bofinger restaurant and Bastille are also within a few blocks. The owner is very easy to work with and the apartment has always been very clean. The Place Des Vosges, ( a famous beautiful park) is only a few blocks away as well. Notre Dame is about a 15 minute walk. The Pompidou is an easy metro ride. I can not say enough good things about this place-truly! In fact we are returning for 2 weeks in June! Renting a place is so much better/cheaper than a hotel considering how long you will be there. The owner is Stephane Gautier. You can find his website at holidaystudio.fr. I would check it out soon as he books up pretty quickly. Have a great trip!!

"Isle St. Louis (1st district or arrondissement)"

I hate to correct Kent, but Isle St. Louis is in the 4th arrondisment.

There are plenty of nice markets in the higher numbered arrondissements -- the Marche Aligre (12th), the Marche Bastille (11th), Batignolles Organic Market (17th) so if you see an apartment that you like in a higher numbered arrondissement, there will be markets and restaurants. Some of the best restaurants that I have been to in Paris have been in the higher numbered arrondissements. If you are willing to explore public transportation, you might find that you get some significant cost savings if you look in a higher arrondissement that is not quite so much on the tourist radar.

With two weeks it doesn't matter where you are given the great transport. I would look for a nice neighborhood and there are dozens. Look for an apartment that appeals to you and then google walk the environs and check out that particular neighborhood. We have stayed in the 4th, the 5th three times, the 7th, the 11th, the 14th, the 17th three times, the 18th three times and the 20th. We loved them all except the 7th and we were not that wild about the part of the 11th we were in. I am sure that every arrondissement has nice areas. It is nice to be near the river on a first visit; those evening strolls are sweet.

I am going to second JHK. I rented a small one bedroom apartment a half-block away from rue Montorgeuil for the month of October last year and was amazed to discover rue Montorgeuil-had never been there. I was trying to get out of my comfort zone by renting in the 2nd arr. (not normally a tourist destination). Rue Montorgeuil has some tourists on it but I found it primarily a French destination with the cafes and restaurants full in the late afternoon and early evening with mostly the afterwork French crowd (weather was unusually warm for this October). The rue leads down to the Les Halles shopping area and it has everything you would expect from a major market street. The metro is Sentier using the Petits Carreaux exit. I also like staying in the 15th near Mo. La Motte Picquet-Grenelle since it is a major metro stop with three lines running through it taking you to just about any part of the city you want to go. It is just around the corner from the Champ des Mars (which is where I like to walk at night to the Eiffel Tower) and there are plenty of shops and eating spots and an open air market under the overhead metro line on Bd. de Grenelle. As JHK said, there are really very few bad neighborhoods to stay in Paris and lots of good advice here. Depends on your priorities.

We have stayed in the 9th in a studio for the past 11 years. It is a 20 minute walk or 15 minute bus ride (stop is outside the door and 50 feet up the road) to the Louvre. Coming back is a bit tricky, but doable. Rue Rodier is one way so the bus cannot go up it. The home bus stop is about 3 blocks over and you walk home. No big deal, if you know where to get off. There is a large supermarket Carrefour (sp) about 2 blocks over. The post office and its ATM is 3 blocks. A nice park is 1 block, the Metro is 2 blocks. When there, we live like Parisians. Very few tourists around. However, 2+ blocks away, Pigalle, Sacré-Cœur, with the ensuing tourists and Moulin Rouge begin. There is a food market at Place d'Anvers, facing # 2-10, and Avenue Trudaine (across from #15-17)
Open Fridays from 3:00 pm to 8:30 pm.

http://www.timeout.com/paris/en/shopping/the-best-markets-in-paris would be a place to start looking for markets.