"I thought we were getting along fine until I heard the first explosion."
-- Ministry delegate Royden Poke
The riot broke out in Chipping Clodbury, where talks regarding the Goblin Bill of Rights were occurring between the Brotherhood of Goblins and the British Ministry of Magic, when Goblins who had acquired wands started using them to wreak havoc.
The rioting Goblins caused some items in the Muggle town to explode, transfigured other items in wildebeests, and called for justice for their kind (DP3).
Because the riot was reported in the 1 June issue Daily Prophet article "Goblin Riots Erupt in Chipping Clodbury", it mostly likely occurred shortly before June 1st. The timeframe for these events is c. 1993.
Chipping Clodbury is a fictional place, but Rowling was born in the English town of Chipping Sodbury (Wikipedia).