Paris in April
I am also going to be staying in the 7th in May. I agree with all of the Dodo'ssuggestions, they are all moderately priced, with really good food. Au Bon Acceuil is great, especially if the weather is nice and you land a table outside with the spectacular view of the tower at night. A walk to the Eiffel Tower after dinner is a great idea in nice weather. Walk along Rue Cler and stop in the speciality shops, you will find everything you need for a picnic lunch.Maison du Jambon has amazing pate' and gourmet foods to go.Oliviers have all sorts of oils and goodies to take back home with you. I brought home the most amazing white truffle oil from that store.
Cafe du Marche has a very inexpensive lunch menu, blackboard plats du jour, that usually run about 8-9 Euro, very generous protions. here are few I have eaten there, chevre salad served with 2 huge peices of warm goat cheese over a huge bed of greens, a garlicky duck leg served with frittes, steak tartare. The place is packed, and with tables outside you can sit and watch everyone strolling down Rue Cler, it is so Parisian.
On Rue Universarity there is a great chocolate shop Michel Chaudin. You will enjoy the area, and be in walking distance of so much, you will be able to burn off all those calories!! Enjoy!!!
Little ity bity place called La Gavroche, which is actually in the 1st Arr, but 7 is close to 1 and very walkable. They don't speak english, I hope that is what you are looking for.
19 Rue St-Marc
Tel: 01 42 96 89 70
In addition, actually in the 7th Arr (all bistro types):
La Fontaine de Mars
129 Rue St. Dominique
Tel: 011 33 1 47 05 46 44
I would suggest a reservation if you can get it, they were very busy when we went.
Atelier Maitre Albert
1, rue Maitre-Albert
Le Petit Troquet
28, rue De L'exposition
This one is non-smoking, can you believe it?
Au Bon Accueil
14, rue de Monttessuy
La Grange Bateliere
16, rue de la Grange-Bateliere
15, re de Babylone
This one may be a bit more expensive
In the 6th Arr, there is a grocery called La Grande Epicerie inside Au Bon Marche for specialty goodies like champagne, oysters, cheeses, fruit, pastries etc...
In the 8th Arr, Bistro:
133 blvd Haussmann
if it is still there great view, wine bar with full menu.
Don't miss Laduree for pastries if you are anywhere near.
16 Rue Royale
And, finally if you are in the 15th Arr:
Le Troquet - Basque
21, rue Francois-Bonvin
Le Tire Bouchon (tiny, but worth it
)62, rue des Entrepreneurs
22, rue Fremicourt
The 7th arr. while pretty quiet at night (no movie theaters except for La Pagode, no night clubs, etc.), it's hosting a huge number of wonderful small neighbourhood bistrots. You should start doing your homework. Read yourself through the forum to start with.
Local market: Rue Cler, obviously and Rue de Breteuil.
Bakeries: Not what is missing in the 7th. Poujauran, Millet, Lenotre, etc.
Cheese: Marie-Anne Cantin, a cheese heaven!
Bistrots: Le Florimond, Le P'tit Troquet, Café Constant, Les Fables de la Fontaine, Pasco, Au Maupertu, Au Bon Accueil, Le Clos des Gourmets, Le Sancerre, Au Pied de Fouet, L'Esplanade, Le Tourville, Thoumieux, Chez Les Anges, La Fontaine de Mars, Le Vauban, Bistrot de Breteuil, Oudino, and so on. You'll find comments on almost all of these, if you search here.
BTW, a title like 'bistrots and markets in the 7th' or so would have been a lot more appropriate, since all these places will still be there in May... at least, this is what I do hope.