Nero (37-68 AD) was the Emperor from 54 to 68 AD. He was no light weight and we know what he got up to from Tactius, Suetonius and Cassius Dio. Tactius talks about how Nero blamed the Christians for the Great Fire of Rome in 64 A.D and from that point the Christians got persecuted a bit in Rome. (I have previously mentioned this Tactius quote before and made some further comments on it).
The thing is, Acts doesn't mention anything about this. Some might think this is because Luke liked cutting down the tall poppies and never talks about rulers in the area, but as a quick example Luke mentions: Sergius Paulus (ruled 47-? AD) the proconsul of Cyprus (Acts 13:7); Gallio (ruled ~51-53 AD) the proconsul of Achaia (Acts 18:12); Felix (and his first wife Drusilla) (ruled 52-58 AD) the governor of Judaea (Acts 23:24, 24:22-24) and how Festus (ruled 58-62 AD) replaced him (Acts 24:27); and that Claudius Lysias was a Roman Tribune (Acts 23:26). Luke actually mentions lots of names, titles and places which means he puts his writings the chopping block of history and lets anyone (or blogger) take a swing at it. In fact Sir William Ramsay in the 1890's set out to disprove Acts as a first century document, but when he went over and looked at the archaeological and historical evidence he changed his mind. In his first chapter to St Paul the Traveler and the Roman Citizen Ramsay said:
I may fairly claim to have entered on this investigation without any prejudice in favour of the conclusion which I shall now attempt to justify to the reader. On the contrary, I began with a mind unfavourable to it, for the ingenuity and apparent completeness of the Tübingen theory had at one time quite convinced me. It did not lie then in my line of life to investigate the subject minutely; but more recently I found myself often brought in contact with the book of Acts as an authority for the topography, antiquities, and society of Asia Minor. It was gradually borne in upon me that in various details the narrative showed marvellous truth. In fact, beginning with the fixed idea that the work was essentially a second-century composition, and never relying on its evidence as trustworthy for first-century conditions,.
Regardless of how right Luke got other peoples names and titles right it still needs to be pointed out that Luke doesn't mention any Emperor at all. But, likewise with the siege and fall of Jerusalem, or the death of prominent early Christian figures, the Roman persecution of Christians isn't mentioned in Acts. This might not be seen as a big deal, but if you were giving an account on the first generation of Christians and how they went under the ruling class, it is a bit strange not to mention the persecution of the Christians in the Roman Empire. James and Peter both write to Christians who are part of the "dispersion" (James 1:1, 1 Peter 1:1) which most people think is a reference to the Christians fleeing from the Romans. James and Peter mention it, because it had happened, Luke may not have mentioned it as it hadn't happened yet.
Overman finds this argument from silence compelling that Acts was written before 64 AD. He also quotes another guy to make his case:
Luke gives no indication whatsoever of the slaughter and massacre of Christians under the Neronian persecution of AD 64. John A. T. Robinson, in examining this remarkable silence, rightly concludes that the burden of proof is on those who would maintain that Acts was composed later than AD 62:
The burden of proof would seem to be heavily upon those who would argue that it does come later, and there is nothing, as far as I can see, in the theology or history of the Gospel or Acts that requires a later date if the prophecies of the fall of Jerusalem do not. From the internal evidence of the two books we should therefore conclude (as did Eusebius) that Acts was completed in 62 or soon after, with the Gospel of Luke some time earlier. (p 96-97)