Some just pointers to get you on the right track and make sure you don't miss out...

 1. The Peninsula Hotel - it's a piece of HK history; Japanese handovers, expensive tea, big yellow hats and much more- go early (11am) if you want to spend ten bucks for a cup of tea and an orchestral quartet or later just to watch the absurdity of it all, then take an elevator to the top floor to Felix....great view
 

Oh and while you are there ask the concierge to give you directions on how to get to the Dragon's Back hike near Shek Oh. They will be able to provide clear and concise directions to this amazing walking trail which tight ropes its way along the mountain ridge of Hong Kong island. Once on the hike follow the signs for Dai Long Wan Beach (Big Wave Bay)...on a sunny day it's one of the best things in the city. Try the Mexican wrap at the beach side food stall ;o)

2. The HK History Museum. If it rains (which it always does in HK) it's actually a really great experience; only a year or so old

3. Mongkok - take the MTR to this station, there's a map in the station and you should just walk around the general area looking for the Ladies Market, the Goldfish Market, the Bird Market and the Flower Market. Mongkok actually looks like the Hong Kong you would expect.

4. The Star Ferry - it goes from the waterfront at Central or Wanchai and finishes in TST; night time or on a clear day it has a pretty amazing view of the island.

5. Wanchai Wet Market - take the MTR to Wanchai station, it is on from around 5pm to 9pm on weekdays and all weekend 

6. Take a tram from one end of the island to the other!!!

7.The Museum of Coastal Defence is beyond North Point but well worth a look. Easy directions on street from MTR station, 15 minute walk.