Belfast's reputation as a dangerous city is often exaggerated. A recent study by the United Nations International Crime Victimisation Survey (ICVS) shows that Northern Ireland has one of the lowest crime rates in Europe. The majority of incidents are committed by local people against local people, unsurprisingly following religious, sectarian or political differences. Tourists are outside this culture and should not be very concerned. As with any other city, it pays to be careful and always be aware of your surroundings. Do not flash valuables or money or walk around reading your guidebook or map. If you need directions, ask in any shop or bar.
There are areas in Belfast which have been scarred by trouble in the past. Though these areas are largely safe to visit, it is important to be aware of where you are. In nationalist areas of the city, it would be foolish to wear a Glasgow Rangers, England, or Northern Ireland football jersey. In unionist areas, wearing Glasgow Celtic, Republic of Ireland and Gaelic Football (GAA) jerseys would almost certainly lead to trouble. Though this is unlikely to affect tourists, it is best to avoid wearing green or orange or the name of any area, especially Northern Ireland, Republic of Ireland or England.
Image: City Hall, Belfast
The City Centre is generally a safe area and is also regarded as a neutral zone. Avoid leaving the main streets at night and try not to venture into dimly lit streets.
North Belfast is not usually on the tourist trail but is becoming increasingly popular with the more adventurous traveller. Tiger's Bay is a unionist enclave which is generally safe during the day but should be avoided at night. The New Lodge, a nationalist area, is similarly patchy and probably best avoided altogether. The Antrim Road (including Carlisle Circus) and Shore Road areas are best avoided at night. The Limestone Road is an interface (on one side is a nationalist area, the other a unionist enclave) and should be avoided at night due to occasional violence. It is best to avoid the nationalist Ardoyne area at night, especially the interface area which links it with the Crumlin Road and Shankill areas of the city.
West Belfast is perfectly safe and generally tourist-friendly during the day as long as you don't venture too far from the main roads. Do not venture off the Falls Road at night. The Shankill Road itself is best avoided especially at night. The nationalist Turf Lodge estate in Andersonstown is best avoided altogether. Falls Park and the area around it is dimly lit at night and is best avoided. The Crumlin Road is a unionist area and is generally safe during the day but not at night. I also suggest tourists don't write on the Peace Wall not because it is dangerous to do so but highly insensitive to do so. Messages like "tear down this wall" etc are not appreciated by the locals - the wall is there for a reason so be sensible and don't do it !
South Belfast is the most affluent part of the city and is generally trouble-free. Student night life can lead to altercations outside the bars and clubs on Bradbury Place at night. Sandy Row is a unionist neighbourhood that would probably be best avoided at night but is perfectly safe during the day and usually very quiet. The unionist Village area which lies further on from Sandy Row between the Lisburn Road and Boucher Road is quiet and residential but best avoided at night. The mixed Holylands and Ormeau Road areas do not deserve their reputations as trouble spots as they are generally both very quiet other than the occasional student party.
East Belfast is a predominantly unionist, working-class district that suffers from the same social problems as similar areas in other cities in Britain and Ireland. The Newtownards Road is generally safe and well lit at night. One potential flashpoint is the interface with the nationalist Short Strand neighbourhood. Though fairly well kept and safe during the day, it is best to avoid this area at night.
Perhaps more importantly, it is not advisable to make any overtly political statements about Northern Ireland, even if you think that your comments will align with the views of the people to whom you're making them. Otherwise, ask locals for advice and enjoy the hospitality of the majority of Belfast people. If anyone asks your opinion (unlikely as it is taboo to keep the peace but still just in case), say you don't have one and don't pay attention to politics.