The large blocky building next to the church is the former abbey's 13th-century tithe barn, the place where people brought their obligatory contributions to the church, usually 10% of whatever they produced. This particular one has had a chequered history (it was a 17th-century theatre and a 20th-century disco, among other things) but has recently been fully restored and converted into an excellent heritage centre and a food hall focussing on locally sourced Welsh products.
Pride of place goes to the Abergavenny Tapestry , produced by 60 local volunteers over six years to mark the new millennium. Within its 8m width it depicts the history of the town; look for faint messages from the stitchers in the borders. Elsewhere on this floor a combination of artefacts and touch-screen monitors tell the story of the town and the abbey in an excellent interactive display.