No, Sydney does not have a nuclear power station. Australia does not have any operational nuclear power plants.
Lucas Heights
Sydney Parade railway station was created in 1835.
North Sydney railway station was created in 1932.
The main station before Sydney Central was the original Sydney Station, opened on the 26th of September 1855 and replaced in 1874.
Central Station.
Cooper Nuclear Station was created in 1974.
Hartlepool Nuclear Power Station was created in 1983.
There is only one nuclear power station in Sydney, which is used for research purposes. Other than this they play no role in providing power in Australia. Australia does however have the resources of uranium for it but export the majority of it to China.
Chapelcross nuclear power station was created in 1959.
Chapelcross nuclear power station ended in 2004.
Yangjiang Nuclear Power Station was created in 2013.