Paceville is where you go for clubs and late bars; Spinola Bay is where you go for something more relaxed. The waterfront restaurants along Spinola double as bars after dinner, and the outdoor seating on the quay fills up on warm evenings. For something more characterful, the older bars in the streets between Spinola Bay and Paceville tend to be more local and less overtly tourist-facing than the Paceville strip.
Malta produces a few decent local beers (Cisk lager is the standard), and the local wine — particularly from the Meridiana and Marsovin producers — is worth trying if you are staying for a few days.