On HK Island LKF, Wan Chai, Causeway Bay and Soho are the main entertainment areas. LKF and Wan Chai tends to be mainly bars, while Causeway Bay and Soho have most of the clubs.
I'm not sure what you call cheap drinks but there's a 'Bar 7-11' at LKF where you can buy drinks and drink them in the street. As for drinking at the bars, the ones at Wan Chai are generally cheaper than LKF or Soho. For clubbing afterwards, I'd recommend you check out
www.hkclubbing.com to see whats on.