Mon Balzac is a good place to eat and drink,  and spend the evening listening to some soothing music. Staff are friendly. Overall a very warm and friendly place which is just off Dlugi Targ.

Website

 

Velevetka is a small restaurant in a cellar just off Dlugi Targ. Nice food at good prices. They may not have an English menu there, but you should be able to order your food with little trouble.

Website

 

Zeppelin is a nice restaurant on the main floor of the Hotel Wolne Miasto (Free City Hotel) serving traditional Eastern European dishes.

Zeppelin Restaurant