Donghai Island, the fourth largest island in China, is about 1.5 hours drive from Zhanjiang and is popular for its beaches. Buses leave regularly from the Xiashan District.
There are almost hourly buses to Guangzhou, the provincial capital. Buses also leave four times a day for Zhuhai, where you can easily cross into Macau.
There is a train to Hainan Island that originates in Beijing and will take you from Zhanjiang to either Haikou or Sanya. It is about eight hours to Sanya, the southernmost Chinese city.
There are also regular trains to Guilin in neighboring Guangxi province. The ride takes about eight hours.