St Peter's Church on Market Hill is a fine 15th-century wool church that now serves as an arts centre. The medieval fabric is entirely intact — the tower, the nave with its timber roof, the Perpendicular Gothic windows — and the building's conversion to cultural use has been handled with care, preserving the atmosphere while making it a working venue.
The current programme runs from classical music to community theatre to art exhibitions. Check the schedule at the Sudbury Arts Centre website before visiting — the building is most rewarding when something is on. Even without an event, the exterior and the market square setting justify a look.