While St. John's is generally regarded as a safe city, recent increases in the crime rate have been reported. Panhandling is very common in downtown, however simply replying "no" or ignoring those individuals usually does the trick, while a few more may be more persistent. Very rarely will these people become violent, and are usually not a problem.
As in any other city of comparable size, use caution when traveling after dark. Common areas to avoid include Buckmaster Circle, Old and New Penneywell Road, areas immediately around Hamlyn Road, Livingstone Street, Water Street west Springdale Street west to the beginning of Waterford Bridge Road including Victoria Park after dark, and Shea Heights. Most of these places are not areas which tourists would normally be in, and shouldn't be a huge problem.
Caution should be used when on George Street, especially on Friday and Saturday nights. With excessive drinking and drug use, there is a high tendency for people to turn violent. However, it's unlikely that you'll fall victim to a violent assault if you keep out of trouble. Extreme caution is to be had at 24-hour restaurants and convenience stores across town, especially in the downtown area. Violent patrons from George Street often stagger into such restaurants after last call and can be violent, sometimes attacking unsuspecting individuals. As well, a recent rise in armed robberies in the metropolitan area have left 24-hour convenience an easy target for criminals.
However, with crime rates much lower than the national average, little is to fear about walking around St. John's at most times of day or night. With exercising some basic caution, there is no reason why your visit to the city can't be a safe one.