When traveling I usually try and avoid the big shops. Chanel in Paris is pretty much the same as Chanel in NY, Dubai or HK. So unless I have special requests to fill, I prefer to buy from mom & pop stores, craft fairs and seasonal markets.
While it's easy and convenient to buy stuff online, it's not quite the same as picking up a Nepalese watershawl in Nepal, an alpaca scarf in Peru, or Murano glass earrings in Murano.