Where the Places of Coronations

well , for the Archbishop of Canterbury preforming the ceromony. That tradition comes from way back. The origional Archbishop was St. Augustine. He was sent to organize the church for the pope. In creating two provinces (north based in York and south based around london with Canterbury becoming the center) he set the fondations for the upper hand that canterbury holds.  He became the senoir bishop.and as such he crowns the king to show the symbolic long assosiation between church and monarch. For most of the time the bishop would have been the closed advisory( not always though) . Not all king(or queens) where crowned by the Achbishop af Canterbury, william among was crowned by York but it tends to lend legitamicyif Canterbury does it.

As to Westminister Abby - when it was rebuilt by henry III in the 13 centery it was done for among other reasons to house the coranations and burials of kings.