If you're studying Mandarin, it's a different story; indeed in Hong Kong, you can't practice it at all, while Shenzhen is Mandarin-speaking. And the multiple-entry will get you quick access to the Mainland. The fact remains that Shenzhen is ugly as hell though.
City life: a good insider tip is going up the Mid Levels escalator around noon, up to SoHo. You'll find it escalator right next to Stanley Market in Central; it's the longest escalator of the world. All Hong Kong goes up there to have lunch, and going with the escalator, restaurants to the left and right, is quite a sight to behold. Good lunch deals everywhere too.
Taking one of the ancient trams along the northern coast of Hong Kong island is also very nice, it gives you a good idea about the districts the tram travels through (from Kennedy Town via Sheung Wan, Central, Admirality, Wan Chai, Causeway Bay, and further).
Plus the "standards" like Peak Tram, Star Ferry, but you don't need me to tell you about those.
If you have time, go to Stanley, a village on the southside of the island. Very relaxed, some good bars, a nice market and a good museum inside the old colonial structure called Murray House near the beach.
Museums: The museum for history is the best in my view; very much worth visiting even for someone not connected to Hong Kong. Good displays and a great insight into all the turmoil the territory went through during its short history. The other museums are IMO not attractive enough to spend time at during a short visit.
Shopping: Central has the best and most expensive shopping; the malls are all connected via footbridges and tunnels. Women can spend days there, but there's the occasional good offer too. If you're looking for electronics, give the tourist stalls in Tsim Sha Tsui a berth, they rip you off in numerous ways. There's a great electronics mall in Admiralty, right next to the large sportsground, where they only sell top quality. Or Shenzhen, but be even more careful there!
Nightlife: Lan Kwai Fong is all you need for a short stay. It's a bar street in Central, within walking distance of the Star Ferry Pier. The masses of party people flocking there will guide you the way. I like the Hong Kong Brew House, at the very top of the street. But the other bars are also good, some even sell German beer.
Wan Chai is also exciting, but more spread out, gloomier, more prostitution etc, so there you'd need more insight knowledge to have a truly good time.
I hope that helps - any more questions, do ask.
Samson was a biblical tough guy, but his dad Samsonite was even more of a hard case.