Unless you are staying in one of the main cities along the coastline there isn't much in the way of nightclubs on offer. Each village has it's own trattorias and cafes which may stay open late until 1am in the summer. Alternatively you can gather a few mates and head down to the beaches with a guitar, a few bottles to share and party under the stars.
Wildlife areas
Blue Marlin Café (Vernazza) Via Roma 43
Mar Mar café (Riomaggiore) Via Colombo 234d