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.
There's plenty of lovely designer stores in that area of the resort - prices aren't shockingly cheap, but you're guaranteed to get something you won't see at home.
If you're really set on a good shopping trip I recommend you get a taxi from your hotel to the Safari shopping centre and Parque Santiago area, spend a good few hours browsing round there (believe me you can make a good few hours of it...) it's nice and flat in that area so you should be OK if you take it easy, and then get a taxi back 

