Hoi An is a typical fishing village with a mixed history of Chinese, Japanese and French occupants. Declared a UNESCO site the village now welcomes tourists by the bus load. Archeologists can date the village’s first occupants back 2,000 years and the port has always been a valuable asset to whoever controlled it at the time. My Son is an ancient Cham Temple in disrepair now covered in tree roots and vines. The oldest Buddhist Pagoda in the city is Chuc Thanh a temple from 1454 with three arched entrance gates. Close by are the Phuoc Lam Temple (with the Buddha as a boy statue) and the Le Hong Phong.
Try seeing the Thanh Ha Pottery Village where you can watch the potters at work and also buy their local crafts to take home after your trip. There is a market in the city as well as a ferry which will take you from the Bach Dang to Cam Kim Island. You can travel around the picturesque island which is largely unspoiled and also take a tour of the wood carving studios and stores. Cham Island is also worth the ride out there to see the Pagodas and temples. For the best beaches try Cua Dai and An Bang Beach.
For museums in Hoi An take a tour of the Museum of History and Culture of Hoi An, Sa Huynh Culture Museum which is next to the Quan Cong Temple; The Museum of folk Culture or go see the Museum of Sa Huynh Culture and the Museum of the Revolution. There are also a few historic homes in Hoi An like the Phung Hung House (embroidery) and the 200 year old Tan Ky House. There are also Assembly Halls where business men used to meet.
If you have only a little time while staying in Hoi An, consider taking the Cultural tour which gives you entrance into several of the city’s main sites.