Seems that when the fire started, he wasn't even in Rome, he was on vacation about 35 miles away. When news of the fire reached him, he went back to Rome to coordinate efforts to get the fire back under control.
It would seem that enemies started the rumor; they wanted people to believe that Nero started the fire and that he partied while the deed went down.
It's amazing how many lies like that one end up being reported as historical fact. For instance, most of us learned that Rasputin was nearly death-proof. According to many history books, he failed to die after being tricked into drinking poisoned wine and eating poisoned cakes; survived several gunshot wounds; lived through being beaten with clubs; was chained up, wrapped in a carpet, and thrown into the frozen river - dying from drowning only after he had broken free of his chains and escaped the carpet. An autopsy at the time even confirmed it. However, it's probable that this entire account was a fabrication on the part of his killer, Prince Felix Yusupov. The thinking is that Rasputin died of a gunshot wound to the head, and that all the other business was something Yusupov made up to make his actions look justified - certainly he'd done the world a favor by killing someone who was, apparently, too evil to die. In fact, the whole business about his death is fishy... Yusupov's account changed a bunch of times, they were never able to pin down just how many times Rasputin had been shot, and by what weapons. According to Wikipedia (and the more legitimate publications listed in the citations section), there's a decent pile of evidence that Yusupov was acting in collusion with the British Secret Intelligence Bureau. Dude.
Another framed historical figure was Marie Antoinette. She never said "let them eat cake." Again, according to The Book of General Ignorance, the phrase "had been in use in print as an illustration of aristocratic decadence since at least 1760."
Catherine the Great, according to HowStuffWorks.com and Snopes.com, was not killed while getting it on with her horse. She and the horse had a loving, consensual relationship, but the horse's enemies accused him of killing the love of his life to further their own political ends. Actually, Catherine was accused of being into the kinky stuff with her barnyard friends throughout her life, and it was likely just an attempt by her enemies to discredit her or make her look insane - there's no evidence at all that she did the deed with her steed.
But back to our buddy Nero for a moment. He may not have been playing a pretty ditty while burning down a city, but he did have some interesting hobbies. Seems he was something of a drag queen - he loved to sing, dance, and act while dressed as a lady. Also, he had his mom killed and liked orgies. But who doesn't? Have their moms killed, I mean.
By the way, remember how last week I said that fiddles and violins are the same, and that it's the playing style that differs? I wasn't able to articulate what that difference was, but a few days ago a friend did that for me: a violin sings while a fiddle dances.