The Tobacco Factory Sunday Market runs every week in the courtyard and ground floor of a converted Victorian factory in Bedminster. Bristol's less-covered south bank neighbourhood. Local producers bring bread, cheese, fruit, vegetables, and street food from 10am; by 11am the courtyard fills. It's a proper neighbourhood market, not a tourist one.
The Tobacco Factory itself is also one of Bristol's best independent theatres, worth checking the programme if you're in town on a Sunday and staying through the afternoon.