Ian [above] is wrong, Dudley has never been in Staffordshire. As another contributor noted it was an enclave of Worcestershire and remained so until the 'West Midlands' conurb was formed. The County Cricket ground [sadly gone] was a home ground for Worcs. until the 1970's and derby games against the Bears [Warwickshire] were always well attended and hotly contested.
The Staffordshire border ran alongside the Crooked House pub just west of Gornal at one end and along the Tipton Road to the east.
Quarry Bank, though technically part of Dudley Borough, was in Staffs traditionally and was the home of the great traditional singer George Dunn.