What to buy:
SOBAOS and QUESADA are tipical Cantabrian cakes, very popular among both locals and visitors. Do not leave without tasting them!
They are original from the the Pas valley, nowadays spread through the whole region.
In Santander a good place to buy them are Confiterias Gomez, but you can find them in every shop and market too.
A giant department store with everything under the sun. Includes a grocery store on the first level and a movie theater. More of a mall than a department store, except that it's all one company.
What to buy: Mostly standard department store stuff, but there's a shop in the basement with some very nice nautical items, as one would expect in an oceanside city like Santander.
In downtown there are small supermatkets where you can buy food. There are still some of the old fashion small family run shops where you have interact with the clerck to buy things. Enjoy them while they last!
Spain in general is known for having good leather. In Santander you can find many show stores offering high quality shoes at a good price. The main shopping area is in downtown, around the twonhall or "ayuntamiento".
If you are looking for clothes you will find plenty of stores specialized in young clothing (targetting mainly girls, big surprise ...)
In the outskirts of Santander there are some big stores (like malls) where the locals go to do most of the shopping.
The best is "El Corte Ingles" specially for clothes although is also more pricy than the other malls.