There are lots of local initiatives to bring some of the traditional arts and culutre of Hoi An back to life. No doubt many of these are targeted at tourists - but it is still great to see that tourism can sometimes contribute towards the revival of traditional art forms. To see traditional dance and theatre - head to the Hoi An Traditional Performance Theatre located on Nguyen Thai Hoc Street.
The theatre is in the building right next to the street. It is completely open to the street so even if you don't pay for the tickets you can still take a peep at the shows. But the tickets only cost VD100,000 so it would be much nicer to pay up and support local culture. The show is around 30 min and include traditional dances, short snippets of traditional plays, and some games. There is even a lucky draw in the form of Vietnamese Bingo.
At the back of the theatre is an arts and craft shop with a craft gallery on the 1st floor. It is worth a visit to see some of the traditional crafts in Hoi An. There are some very beautiful designs showcased here.