Right near your hotel is a marvelous gourmet food store. I highly recommend it: Fauchon grocery stores. Ask your concierge for directions.

A couple of tips...
1) The metro is not a safe haven. It is great if you wear a money belt, do not flaunt your cell phone or purse. Use it but be careful. Use only cabs at night.
2) Use your concierge or tour guide to recommend good restaurants. The French rarely cook at home and often take out, so most neighborhood places are excellent and the concierges can recommend some that we and the guidebooks don't mention. We have never been steered wrong by a concierge in Paris.
3)One special thing to do for a few hours on a Saturday or Sunday is go to the elegant flea market in a horrible area of Paris. Wear a money belt! It is a wonderful experience.

Puces de Saint-Ouen

Open on Saturday (from between 8 and 9am to around 5:30 or 6:30pm) and Sunday (from about 9 or 10am to 5:30 or 6:30pm), as well as on Monday (from between 9 and 11am to 5 or 6:30pm) – all times very ish – Saint-Ouen’s flea markets are just to the north of Paris, M° Porte de Clignancourt. Take your time to wander around and enjoy the atmosphere, bearing in mind that Friday is “dealers day”.
What I like about this flea market, the biggest in the world, is the sense of being in another place and time, far away from the “real” world. You’ll have a sense of being removed from everyday reality, and the more you wander, the better it gets. This may compensate for the fact that you probably won’t find super bargains here, although the prices are lower than inside Paris proper. You also have all the advantages of buying from authorized dealers (like – if anything comes up later, you know where to find them!).
The official market is organized into sub-markets, each with its own character and ambience. City walls used to separate Paris from its outskirts, and many of the poorer people who lived on the “other side” sold junk and old clothes to survive. Plus, there, they escaped city taxes! By the 1880s customers were already coming from the capital in search of secondhand items. Around 1920, when the walls were destroyed, the dealers organized themselves into official markets and sub-markets. As you browse around, you’ll also spot private businesses among these.