Venue with food around the centre of Stafford (4)
I believe the answer is:
caff
'venue with food' is the definition.
(cafe)
'around the centre of stafford' is the wordplay.
'around' becomes 'ca' (circa).
'the centre of' says to take the centre.
The middle letters of 'stafford' are 'ff'.
'ca'+'ff'='CAFF'
(Other definitions for caff that I've seen before include "Eating-place" , "eatery" , "snack bar" .)