Langkawi's main town is Kuah, although it's not really all that big. The town lines a long curving bay with the ferry terminal and yacht club at the south end. Next to the ferry terminal is Eagle Square, Dataran Lang in Malay. The square is dominated by a huge statue of a brown eagle built on a pier extended into the bay.
The large eagle statue in Kuah harbor
The square is surrounded by arcades covering small souvenir carts and food stalls. The square is especially popular in the early evening as it cools off quickly from the heat of the day. The reasoning behind the brown eagle stems from one of many theories about the island's name. 'Lang' means eagle in Malay (although the modern word is actually helang) and 'kawi' means reddish brown - or the brownish limestone that makes up the island according to some.
Next to Eagle Square along the waterfront is Lagenda Langkawi, the 'legends of Langkawi', a sort of cultural park of gardens and handicrafts. Admission is RM 5 for adults, but it's a sight I'd recommend giving a miss.
Across the main road and up a bit is Langkawi Fair, about the only shopping mall on the island. You'll find several batik and handicraft shops here, as well as a McDonalds (if you must) and some duty free shops.
In the center of Kuah you'll find and area of four or five square blocks of shops selling batik, local handicrafts and duty free goods, as well as banks and restaurants. A road just south of the city center is the site of a night bazaar several evenings a week. Most of what is on offer may be interesting to see, but there isn't much that's really aimed at tourists.