A great way to see the city and get around cheaply is to take a motorbike taxi. Of course, it is more dangerous than the bus or a taxi, but it is much faster than either and only a little more expensive than a bus ride. You can ride 3-5 km for 5 yuan. Make sure you bargain! A good tactic for bargaining that has worked well for me is to walk away when the driver won't give you the going price. Usually they will give you a fair price after you feign not giving him/her your business. Of course it is tough to know the going price if you are new to the city. You can judge how expensive it will be by taking a taxi. It should always be cheaper than a taxi ride. I have made friends with some of the drivers and call them when I can't seem to find anyone else to give me a ride.
When you're at Zhongshan and ready to leave the city, there's a bus station right next to Fuhua hotel. You can't miss it if you just ask a bellboy or lobby person where it is. Its literally around the corner. This bus station/stop is a great way out of Zhongshan since it makes stop at all the other major cities near Zhongshan especially Guangzhou.
From Hong Kong there leaves plenty of ferrys to Zhongshan. Trip takes about two hours. From Zhongshanharbour you gto to take a taxi though to get to centrum, it's quite a long way, maybe half an hour by car.
Many ferries ply the route between Zhongshan and Hong Kong (both the China-Hong Kong Terminal and Macau-Hong Kong Ferry Terminal). If you opt to take the ferry from the Macau-Hong Kong Ferry Terminal on Hong Kong Island, there's an 8:20 am crossing. On the return trip, from Zhongshan Ferry Terminal, the last one to the Macau-Hong Kong Ferry Terminal leaves at 8:00pm.