The first thing I would advise you to do is to seek out one of the numerous markets. I had resolved to visit one of the ones listed in our Time Out guide, but a friend and Paris resident recommended Marche D'Aligre near Bastille. Go. It's phenomenal and makes Broadway and Borough Markets look more than a little lacklustre by comparison.
Amazing sauerkraut (?)
In terms of restaurants, I would entreat you to go to L'Os a Moelle (3, rue Vasco de Gama). It's one of Steingarten's favourites, and we ate an extraordinarily delicious and balanced meal there (35 euro for a four/five course menu, excluding wine).
We tried to go to L'Ami Jean (27 Rue Malar), but it was fully booked. I've heard great things though.
Our friend took us to L'Olivier (88, rue Ordener), where we had a good meal served up in hefty portions.
There were a couple of nice patisseries near to where we stayed: Le Moulin de la Vierge (166, avenue de Suffren) does an incomparable coffee eclair and the window displays at Patisserie Traiteur Secco (Rue Jean Nicot) are mouthwatering.