Go down the pub, perhaps — not a nice one? (4)
I believe the answer is:
dive
I believe this clue is a double definition.
'go down' is the first definition.
(diving is a kind of going down)
'pub perhaps not a nice one?' is the second definition.
(as in a dive bar)
'the' acts as a link.
(Other definitions for dive that I've seen before include "Headlong plunge into water" , "Disreputable nightclub" , "Seedy bar" , "Dip" , "Plunge - seedy club" .)