Where is a good place to travel from Xiamen? The kind that doesn't join the group, free travel for about three days.

Shanghai does not recommend it. Because the Bund is under construction. I suggest going to Shanghai next year, which happens to be the World Expo. Shenzhen is a good choice. However, I can't tell you anything interesting about Shenzhen, because it's all man-made attractions. Starting from Xiamen, there is not much time in three days. If you are interested in tulou, you can visit tulou in Yongding and Nanjing. If you are interested in natural scenery, you can go to Wuyishan. If you are interested in ancient towns, you can go to Changting and Peitian.