Cathays, including the city centre, is statistically where the most crime happens in Cardiff. These crimes primarily include anti-social behaviour. Cardiff is smaller and overall safer than most major UK cities. There are rough areas of Cardiff, such as Riverside and Splott, but they are not necessarily more dangerous and are simply more socio-economically disadvantaged compared to other areas.
Wherever you are, exercise caution if you are on your own and try to remain in populated areas.