I've gone ahead and kept this answer split across two comments, because Reddit is very much an ass with lengthier stuff.

Nero is a fairly controversial figure, as we know, and perhaps one of the most notorious Roman emperors. There's countless stories about his corruption and malice, but as you note these largely come from the likes of Tacitus, Suetonius, and those who followed their works; in short, it is a reputation largely given to us by the senatorial elite, who for the most part despised Nero both for his populist style of government and for the extravagant public and private works he constructed across the empire using higher taxes on the upper classes (surprise, surprise: the main reason the rich hated their ruler was because of higher taxes!).

It's worth noting, however, that even these sources themselves don't agree on precisely how bad Nero was, or even the reasons for why he was so bad. To use one of the more famous parts of his reign - the Great Fire of Rome - as an example, there seems to be disagreement amongst the sources of the fire's significance, its cause, and where or what Nero was doing during the fire. We know about the fire from three sources - Cassius Dio, Suetonius, and Tacitus - none of whom were writing contemporarily to the fire. Those sources that were contemporary and talk about the fire, such as Fabius Rusticus, Marcus Cluvius Rufus and Pliny the Elder, have not survived to the present day, but even Tacitus tells us that they were contradictory and exaggerated (hardly a surprise from the latter of these three, who described Nero as an 'enemy of mankind', Natural Histories 7.8.46).

Now, the part that is interesting about the fire is that despite coming to us through sources hostile to Nero, their discussion of what happens after the fire is perhaps telling to why the people might have thought Nero was a good ruler. While Cassius Dio and Suetonius tell us that Nero sang 'The Sack of Ilium' as the city burned (hence the legend of Nero fiddling while Rome burned; Cass. Dio, 62.16; Suet., Ner. 38), Tacitus instead tells us that Nero was in Antium at the time but returned to Rome to organise a relief effort immediately upon hearing news of the fire, paying for the removal of bodies and debris with his own funds, opening his palaces to provide shelter for the homeless, and arranging the delivery of food supplies across the city to prevent starvation (Tac., Ann. 15.39).

After the fire, we know from both Suetonius and Tacitus that he made efforts to rebuild the city in a safer fashion, and make the city safer generally to lower the risk of future fires (Suet, Ner. 16; Tac., Ann. 15.43). While there were rumours that Nero himself had started the fire (eg. Cass. Dio, 62, Suet., Ner. 38; Tac., Ann. 15.38-44), that Tacitus notes Nero's presence in Antium at the time might suggest that there was some other cause beyond Nero's control or inclusion (indeed, Tacitus suggests as much; Ann. 15.38f.), and it doesn't appear to have dampened public support for Nero all that much, especially when considering his actions to reinvigorate and relieve the city after the fact. Shifting blame to the already unpopular Christians probably helped him, too (Tac., Ann. 15.44).

Beyond his efforts after the Great Fire, Nero's popularity with the people is more clearly seen in the East, where he was hailed as 'The New Apollo' and 'The New Sun'. This popularity is likely from the peace that Nero secured with the eastern kingdoms of Armenia and Parthia, who had been quite the thorn in Rome's side for some years. This peace was so popular within and without the borders of Rome that the Armenian capital, Artaxata, was renamed 'Neroneia' in his honour (albeit temporarily). Nero even sent a fortune of 50 million sesterces, as well as architects and construction experts, to rebuild the city after Rome had previously razed it during an invasion in AD 59.

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This is fantastic thank you!