Australian teenager travelling to China with his Chinese girlfriend and her family

It's hard to say how much he will need, as the expense depends much on where they are going to visit, what rate of hotels they are going to stay, etc.
Generally, you can offer him CNY10,000-20,000 for four weeks. If afraid that's not enough, give him a bank card which can withdraw when needed. Most banks in China nowadays recognize overseas bank card. And one is not allowed to bring too much cash into China.