I haven't heard that there is a swimming pool near Nanshan ~ But the price of the big beach behind Shaoxing North Railway Station is 15 yuan every time. There is also the East Gymnasium, which is a little more expensive than the big beach, about 20 yuan/time. There is also a beautiful outdoor swimming pool in the east of the city (get off at Shaoxing High School, No.28 Renmin Road).
There is a Jin Shibao Fitness Center with a swimming pool in Shuigouying. It is good to get a fitness card, but it is not very expensive to get a card for students. However, it's very close to the east of the Ministry of Arts and Sciences ~ Nanshan still has a certain distance ~