Shekou is in the West side of Shenzhen. Since Shenzhen is very long from East to West, so Shekou is really far away from the city center. If you want to go to Shekou from city center, the best way to go is to take a bus K204.
There are two kinds of bus 204, one is the regular 204 and the other one is the express bus K204.
There are two ways connect Shekou with Shenzhen, one is Shennan road, it passes "Window of the World", "Happy Valley", "Shenzhen University" etc. Regular 204 runs on this road and makes all stops on this road.
The other way connects Shekou and Shenzhen is Binhai express way which is K204 used. There is no stop on Binhai express way so it saves lots of time. This well maintained express way also has a great sightsee, it's next to the sea (that's what Binhai means), you can see Hongkong cross the sea.
Since Shekou/Nanshan is away from Shenzhen, it's not easy to go to Hong Kong via Luohu Custome. There is a better way to go to Hong Kong airport from Shenzhou by ferry. Take ferry at Shekou, as soon as you arrive in Hong Kong port, you can check in with your airline so you don't have to take your baggage by yourself. Next, you will get 120 Hong Kong DOLLAR!!! It's airport tax refound, since you didn't stay in Hong Kong so they refound your airport tax.
You may also take ferry to Shekou when you arrive in Hong Kong airport without entering Hong Kong. However, there is no cash refound for this.
For more information and ferry schedule:
Since the taxi is expensive and subway is very limited, you have to use bus in Shenzhen most time.
There are adequent bus in Shenzhen also. If you know their route, they can take you to anywhere in the city. There are two kinds of bus, one is the large bus operate by city transportation and another one is little white van which is private owned. It's OK to use either kind of bus though I still prefer the large bus, I think it's pain to stay in a little van.
Shenzhen is building its subway system now. The subway system is new and looks very beautiful though it is still only reaches very limited places. Taxi in Shenzhen is the most expensive in China, the subway is a very good replacement for taxi.
Shenzhen's bus system is the way to get around the city. There are many different companies which offer routes from almost anyplace to almost anyplace. The main street is Middle Shennan Road. The main bus station is at the border crossing / train station at the southern tip: 'Shenzhen Station.'
Litchi Park and Honghu Park are both free to enter. Large amusement parks cost $10 - $15 (US) to enter. They are located on West Shennan Road via bus 101. They are all worth the time, and plan on going to only one a day because they are large and need time to walk through.