If i were to go back in time and take an extensive walk around ancient Rome, say during the time of Trajan, how likely would i be to get assaulted, killed or robbed outside of the better areas? To which modern cities could the danger of such a walk be compared?
We just don't know. A lot of people will use Juvenal, a satirist of the late first century who painted a very vivid picture of Roman life, to show that the city was very dangerous. However, this is roughly the equivalent of using a modern stand up comedian to get an accurate picture of life in Chicago--I have spent a great deal of time in Chicago and have yet to pay a bribe or get shot, but stand up comedy acts usually revolve around those two aspects. So Juvenal is funny, and he gives a good example of what the grumpy sort of conservative might say, but it isn't very useful in a statistical sense.
So another way people might look at this is whether the conditions for crime exist, although I personally think this is futile as I'll explain later. On the face of it, conditions for crime seem pretty ripe: there was very little in the way of active policing, grinding poverty and copious inequality. But these conditions can also be said to be fairly true for modern Mumbai, which had fewer murders in 2013 (187) than New York City (332), which is quite safe for an American city. Drawing straight lines from a set of observed material or social conditions to crime rate is usually not possible. After all, policemen are not necessarily better at reducing crime than, say, neighborhood organizations like what existed in Rome in the form of vici.
But this brings up an issue that is easy to miss: despite the common comparisons to third world cities, Rome is comparable to precisely nowhere on earth. In fact, this applies to every ancient city, as the industrial revolution and rise of globalization has irrevocably altered every settlement of significant size. There are places in the world where you can find villages or small bands that are relatively cut off from mainstream society and live in comparable material conditions as pre-modern people in comparable communities and then use comparative ethnography to understand how ancient communities lived. But there are no places in the world where you can find a city of a million in such material conditions. It is honestly one of the most frustrating and yet tantalizing parts of studying the ancient world.
That being said, it is possible to look at comparative stats from, say, Tudor London. One problem with this is that these statistics can be notoriously difficult to interpret--this review of Stephen Pinker goes over some of the issues of pre modern crime stats. The second is that crime rates vary wildly in modern cities, so they probably would in ancient ones as well.
EDIT: Wow, this got noticed. A great book on ancient Rome is Steven Dyson's Rome: A Living Portrait of an Ancient City. It deals extensively with the city itself and is pleasantly "fact heavy". I can also recommend books on Roman urban life in general if anyone is interested.
EDIT2: So apparently my quick comment about Mumbai got the most attention, which is great but further questions about that should be taken over the /r/AskSocialScience. Here is a source for 2009 so you know I'm not making it up.
A follow up question How much of a effect did your class have on your safety?