There are many shows in Menacho street, like Zara, Bershka... Etc. In Santo Domingo St. There are also small curious boutiques.
You can buy food in so many supermarkets. There is one in city centre, Eroski, which is in San Francisco square.
best eating is in Elvas, the nearest city of Portugal. (it's only 5 kilometers from Badajoz).
If you want to eat products of the region you can go around the old town, where you will find many bars and restaurants where you can eat iberics and meat of extremadura. Also you can have a small beer with a free "tapa".
La santina is a very good place to stay and have a dish of iberic meat, ham...
La casona de arriba is a very good place to have a beer before lunch, with a small tapa.