For shopping go to Little India near by Kuala Lumpur you will find many shopping malls nearby. When I visit Malaysia, I do shopping only in Kuala Lumpur. Because we stayed only 3 days in Malaysia.
If you are going to Langkawi, remember that it is the only duty free island in Malaysia. You can get bags, chocolates and whiskey at very good rates at several duty-free malls. In Kuala Lumpur, the high end malls are very expensive in spite of the "sale" going on. For best prices try Mydin mall and Haneef Store which are very near each other. Ask your hotel for directions.
For souvenirs and small gifts, try night bazaars. A lot or bargaining is necessary to get a good price at the night bazaars. Quote 40% of the demanded rate and you will get a 50% bargain.
places like Little India, Little China are famous for shopping. Avoid Electronics as mostly fake branded products are sold. Little India is like India with Indian community living there. You can shop for clothes etc. You can bargain.
At Little China the Traders are Rude. Avoid shopping there. It is equivalent to Chor Bazars in India. No guarantee. Here Rule while shopping: If you bargain & agree on a price, BETTER buy it from that shop or Trader. If you do not buy, they take offence & the message spreads in the market & you will not be allowed to shop.
Singapore is better for Shopping though may be little costlier than Malaysia
