Our best source for the Life of Nero is Tacitus The Annals of Imperial Rome. As I understand it there is some debate as to whether Tacitus generally supported or opposed the imperial government. He presented a lot of the emperors like Tiberius evenhandedly. However, his history of Nero's reign is undeniably negative.

• Nero ordered the death of several people (his mother and step brother Brittanicus)
• He reportedly played his lyre while Rome burnt.
• He blamed Christians for the Great Fire of Rome and was the first to persecute them. This, of course, made him less popular in the later Empire.
• He was also considered very vain and bribed the judges in the Olympics to make him the winner.

It's possible that the positive sources of Nero's rule have just been lost. The other sources we have like Suetonius and Cassius Dio also seem to be negative.