The "Pax Romana" was a real phenomenon, as much as one can criticize its definition of "Peace" or how the "Pax" gets confused with an idyllic vision of society free from struggle and strife, the period of roughly the first and second centuries CE were remarkably low in large scale violence by the standards of the region. I do think it is worth keeping that in mind when talking about banditry, crime endemic low level conflict, etc, because one can really only understand this period as a whole if we understand an environment of generally lower violence.

That being said, "less violence than sixteenth century Europe" is a very far cry from "no violence". On the low end, crime was prevalent. We cannot say more than that, and any attempts to quantify an ancient crime rate should be treated with extreme suspicion, but we do know that crime and violence was something people worried about. Most famously the satirist Juvenal said it is simply irresponsible to leave your home at night without first drawing up your will, and while there is plenty of reason to doubt his satires as actual empirical descriptions of Roman life, it must at least reflect present anxieties. There were also bandits outside of the city, this is complicated to discuss because of the way the term latro (bandit, robber) was applied to anyone who resisted the Roman state and thus was conflated with broader phenomena, but at least we can say that travel between cities in parts was thought risky enough that it was best done in a group.

That being said, I suspect you are asking less about a knife in a dark alley and more about areas of general lawlessness, where the Roman state struggled or even failed to establish its authority, and these also existed. One of the more well known examples is Isauria in the south of what is today Turkey, a rugged and mountainous land with inhabitants that can be roughly equated to the Chinese imperial concept of internal barbarians. Several times throughout history the area required full scale military campaigns of suppression and it remained under only partial control well into the Middle Ages. Sardinia is another region, the interior of which is still today called "Barbagia" derived from the Latin "Barbaria" or "barbarian".

Beyond areas we know about historically, there are also regions where the remains of Roman military architecture implies continuous struggle for control. For example, there is a high concentration of Roman "fortlets" (mini forts containing small detachments of infantry and cavalry) along the Exmoor coast, in northern Cornwall. There is no certainty about what their exact function is but they were likely some protection from coastal raiding, perhaps from Ireland, but also perhaps from Wales. Wales itself had a very large Roman military presence, most likely there to protect the mines, but that requires something to protect the mines from. And in modern Romania, the concentration and arrangement of Roman forts around the Carpathian was such that I went to a presentation calling it a "counter-insurgency" deployment.

As far as I am aware there has never been a work trying to bring these all together and describe the "lawless" regions of Rome and the "internal barbarians". That does not mean there is not one though and given current interests in history in general I would be shocked if one was very far away. But absent that we can say yes, there were areas that were not fully or even at all under the control of Roman authorities. Whether that meant they were dangerous or just that you would need to make special arrangements to go there (deal with local "kings" etc) cannot really be said without statistics we simply do not have.