Budapest is definitely a safe city with the proviso that as with any other big city there are some standard precautions you should take, such as being watchful of your wallet or purse, don't flash thick wads of banknotes or expensive jewelry and don't leave your bag or bike unguarded, don't walk alone late at night in unlit deserted streets, don't withdraw cash from ATMs in dark deserted places, don't accept drugs or unsolicited sexual approaches, don't trust people that you instinctively feel fishy, unreliable, way too strange.