Nero was the last emperor of the Julio-Claudian dynasty and has a worse reputation than he deserves.
During his reign, he focused on diplomacy, commerce and attempted to increase the Empire's cultural capital by building theaters and promoting athletic events.
In foreign relations and militarily, he was victorious in the Armenian War and suppressed the British revolt of 60-61. In the year 68, a coup d'état took place in which several governors were involved. After that, he took his life.
Nero was also a fierce persecutor of Christians and not very popular among politicians—to whom we surely owe a lot of his bad reputation. It was said he was an extravagant tyrant who had his mother, wife, and half-brother executed. He also ordered the castration of Sporo to marry him (which is true).
Ultimately, he was infamous for the widespread belief that while Rome was burning, he played his lyre. Actually, Nero wasn't even in Rome at the time.