grid reference TL 975 342 (approximate location)
The Greyhound reportedly stood next door to the Guildhall. Since the White Hart is immediately to the east of the Guildhall, this means it must have been to the west. The building here appears relatively modern, so it seems that the Greyhound is likely to have been demolished.
(Most pub, location & historic details collated by Nigel, Tony or Keith - original sources are credited)