Agree with JohnnyColombia. I was in Cartagena last week and I can confirm that Bocagrande and the old city are safe. I would my daughter let go there. However Cartagena is quite expensive, taxis are safe and charge what was agreed, but sometimes you have to bargain before taking them or just let them go and take another one. I don't find the beaches in the city are good, but the old town definitively is. To start feeling the city at night they could take a chiva (vallenato party bus).