Hong Kong
If you have at least two nights available, Hong Kong is definitely worth a visit. It's one of the most exciting cities in Asia. Fun is guaranteed.
Lan Kwai Fong
It is where most of the night occurs. It is basically a 4-block square of bars where two of the sides do not allow cars. The bars are open and you can easily walk in and out of them. Lan Kwai Fong ("LKF") is located in Central. Get out at the Central Subway stop and look for a road called D'Angular St. Make sure you check out this area. Also, near LKF is a series of escalators that lead you higher and higher up the mountain with tons of GREAT restaurants. The escalator is on Shelley Street. Another cool area to go out was Wan Chai.
Hong Kong Park is worth walking through. The city is incredibly urban, but this part helps display the tropical nature of the local geography. It isn't a MUST, but it is near Central and I thought it was kind of cool.
The Peak
Everyone will tell you that "the Peak" is a MUST. I absolutely agree. Take the Peak Tram from Central to the peak for amazing Hong Kong views. It is great by night and by day. I would avoid eating dinner up there because it is touristy, expensive, and not very good. You won't have time for it, but occasionally, I would walk back down the mountain from the Peak back to Central.
Just walk around Central. You will see the British influence in the architecture and you'll have it juxtaposed with Asian people and HUGE skyscrapers.
Stanley Market is on the opposite side of Hong Kong Island. It was nice to see the island on the way there and it was fun
shopping too.
Kowloon
Nathan Road is sort of the NYC 5th Avenue. Definitely check out Mong Kok. There is a subway stop labeled, Mong Kok. This is where you can buy all the cutting edge electronics. It is INCREDIBLY DENSE with people and shops - the true Hong Kong experience.
The Giant Buddha and the Po Lin Monastery are a MUST. It was one of my favorite things I visited.
Cheung Chau and Lamma Island are also cool islands.
Macau: it's very easy to go to Macau from Hong Kong. You can easily take a ferry and explore a day or two there. Macau is known to be the Las Vegas from Asia. Be prepared to see the cool hotels, shops and places to gamble, all over Macau. Macau is a former Portuguese colony, so it's quite interesting to see the Portuguese influence in the architecture and language in Asia.