Rome was a vast city, somewhat like the New York of its day. Rome was a very cosmopolitan city with people of various ethnicities and religions. Some sectors of Rome was very safe, particularly when the patrician and/or other elite classes resided. Those areas were guarded as it was believed that the lives of such citizens had the most value.
The section of Rome where the lower and/or other disenfranchised classes resided were oftentimes less safe. However, Rome had rules and bylaws which governed crime and other illegal acts. Criminals were harshly dealt according to Roman law. At night time in some sections of Rome, it was considered unsafe to be outside because criminal elements were more likely to be present at that time like it is today in many large cities.