There are hundreds of shopping bargains to be had on Samui at almost every corner of the island. The main shopping sites are in Chaweng, Lamai and Nathon but there are shops worth visiting elsewhere on Samui. Nathon beach usually has the cheapest deals, Chaweng beach the most choice and Lamai beach a nice range of quirky little stores.
Keep your eyes open wherever you are on Samui, all over the island are great and unexpected shopping opportunities. Thailand is famous for its copies of almost everything from watches to trainers to CDs. Most department stores are fixed price but you can bargain almost everywhere else and it never hurts to ask! Just keep it polite and friendly; you and the vendor should both be happy with the final price, if not then just walk away.