What to buy: If you are looking for some traditional products to buy as souvenir to take home, I would recommend both the cheese (Queijo da Serra) and leather products. The cheese is creamy and very tasty, although its flavour is very soft. Leather products are also typical from this area, both treated leather or that leather that looks like natural and still has the sheep's wool inside.
If you want to do some shopping or window-shopping, don't miss some of the pedestrian streets in the city centre, as they have plenty of shops. Also, I've noticed 2 shopping centres in Covilhã, although I didn't visit any of them, and therefore I cannot advice as to whether they are worth visiting or not. One of them is located in the city centre, near the Town Hall, and the other one on the of the residential neighbourhoods, near my hotel and by the McDonald's.