I'd start with a walk through the outdoor market. In years past, the Marché d'Aligre was known for carrying lesser quality produce. It's upped it game, but not their prices as much, in recent years. I think their prices are some of the best in the city; certainly better than in the single-digit arrondissements.
Walk through the Beauvau covered market. There's a shop in there whose name escapes me, but it's full of terrific ingredients, such as tonka beans, which for ridiculous reasons, are illegal in the US. (They're poisonous in large quantities, but you'd have to eat at least 8 pounds of them to suffer any effects). They have really nice olive oils, banyuls vinegar and other only-in-France things.
Blé Sucre patisserie is in this neighborhood as well. If you get there early, they'll have kouign amans, which if you've never had them will make you weep with joy.
The Grainerie du Marché is in the Place d'Aligre and is worth a visit.
Le Baron Rouge wine bar is overrun with tourists, but you might enjoy it if you want to hear some English.
There is an organic boulangerie on the r. Thomas Roussel, but the help has been snooty every single time I've been, so I stopped giving them my money.