If it's a clear day, take the Peak Tram up for a great view over the city. And a ride on the Star Ferry is iconic.
I would suggest a stroll or self-guided walk around Sheung Wan to see the traditional Chinese medicine shops, Man Mo temple, etc. If you've already been to Taiwan, it might not be as interesting, but even after months in mainland China, it was interesting to see a bit of history that was safe from the Cultural Revolution.
Beyond that, I think it's really a question of individual interests. There are some great areas for architecture, shopping, dining, art, history, etc.
If the line for the Peak Tram is really long, like, winding around the block long, do. not. bother. I waited 1.5 hours in line for that damn tram in the freezing cold, and only later did I learn a 5 Euro cab ride will get you up to the top. If the line is even remotely long, go that route instead and take the tram down instead. It's a much, much shorter wait on the way down.
I was there around NYE, so that had something to do with the wait I bet. Did I mention it was freezing ass cold?! Ugh, not a good experience.
I'll ditto the others: Man Mo temple, dim sum, Kowloon side. Cabs are super cheap so if you're really pressed for time you can get around quickly that way.