Find Lan Kwan Fong (LKF) and party for a while.
Peak is nice but touristy. Food at the peak is terrible, but view is spectacular.
If you have never eaten in a traditional Chinese restaurant you should. The menu is a trip and a half. Find some friends and go, eating alone is no fun in a Chinese restaurant.
Find a noodle restaurant. Mak's is a great choice, there are a number of them. Prepare to be crowded, don't care, eat the wonton soup and Chinese broccoli and leave happy.
Find a meat restaurant and eat some spare ribs standing up. Leave happy.
Going to the mall is not a bargain anymore. Mainland Chinese flock to HK to buy real Western goods instead of fakes back home, so prices aren't cheaper than in the US. But going to a 15 story mall itself is a hoot just to experience it. Try the Times Square mall, I'm not kidding, and shop in the watch stores nearby. You can get good prices on Seiko's and many other real watches.
The metro will take you to many islands, try them.
Avoid Stanley market, it's a shoddy fleamarket aimed at tourists.
Take a walk in Stanley park. Lovely.
If you have friends have them take you to a seafood restaurant. Pick your fish and have it served to you 20 minutes later.
After you go to the peak on the tram, take a walk up the rest of the hill. There is a great nature preserve and park UP from the peak that you can walk, with views both to the harbor and towards Aberdeen.
Ride all the way up on the world's longest escalator and walk down. Look it up, it's pretty cool.
Go to Kowloon on a Saturday morning and find the pet store street, the electronics street, and walk a few miles up Nathan road.
That's all I can think of off the top of my head, but I did all that and liked it quite a bit.