Get out and do some shopping man!
Depends on what you want, Causeway Bay has a big sogo but if your into the young fashion there are lots of "Far East + Peninsular + Queensway" shopping centers ard. (Near "Woman's street")
If you are travelling alone then the fastest way to get from the airport to HK Island is to take the airport express train. You can get tickets from booths all over the arrival hall, and you can see the boarding area the moment you exit the arrival hall.
Do some shopping first and then go up to the peak around 5PM and stay until night fall. That way you get fantastic day and night views of the city and the harbour.
Come down around 7:30PM and then go to Kowloon side. You can then watch the light show on HK Island side from Kowloon (Star Ferry Terminal area). The light show starts at 8PM and lasts for 15 minutes, so you can then go for dinner and head for the airport after that.
There is an airport express station in Kowloon also. Taxi fare from Tsim Sha Tsui area to the Kowloon airport express station should be less less than HK$20.