The area is full of charming passages and bordered by Canal Saint-Martin.
Take the rue du faubourg Saint-Denis and have a look at:
Rue des petites écuries
Passage du désir
Passage Brady
Then go to the Town Hall of the 10th arrondissement and go for shopping on rue du château d’eau (1st part is only african hairdressers, 2nd part is trendy bobo shops). On number 39, you will see the tiniest shop of Paris.
You will arrive at Place de la République, the place where striking people are used to join for protests. Take the rue Beaurepaire for another shopping session and you will arrive to Canal Saint-Martin. You can take a boat to go until Bastille or just have a walk, smell the relaxed atmosphere and have a drink before walking back to the apartment.