Many hotels now have a Business Centre which have computers available for the use of guests. In some hotels you can find rooms that come with Internet access for use with your own computer.
Internet Cafes are very popular now in China, and can be found in most places. Prices in these Cafes will be cheaper than a hotel, but they are not as convenient or safe, especially if you stay very late.
Internet access is widely available in China. Most good hotels provide an Internet service of some kind; whether in a Business centre or as part of the room facilities. Internet cafes are numerous and cheap.