It depends on what you're looking for really.The really stylish Safari C.C.(opposite the Mare Nostrum) has some lovely clothes and shoe shops,some more designery than others..(always nice to window shop in the "top end" ones that I can't afford..

There are a multitude of Electrical shops at Americas Plaza,next to the Safari C.C. and also loads in the Parque Santiago area. Some nice jewellers there too and also some cheap souvenir shops. There's also Mango near to the Hotel Conquistador,which is in walking distance of the places I've mentioned.
You won't be too far from any of these places staying in LC.