Do not change money in the streets. This is the easiest way to lose it. Use one of the casa de cambio, if you want to change cash. The best idea is to take money out of the ATM.
Generally speaking the historic centre of Cartagena as well as Bocagrande, Laguito and Castillogrande are pretty save. Use common sense and do not carry any valuables around. Leave your passport (carry a copy of the page with your photo and one of the page with the entry stamp), credit cards and larger amounts of money in the safety box in your Hotel.
Do not take anything of value or more money than you will need if you go to any of the beaches.
The Restaurant Gato Negro is extremely concerned about responsible tourism so if you're thinking about using cocaine during your stay in Colombia, we hope you will consider your decision carefully. You can learn about the drug and its health effects at Wikipedia and see a video showing how it's produced here. The production of cocaine also significantly damages the environment of Colombia. And money spent on cocaine goes directly to support groups fighting in Colombia's internal conflict, leading to assassinations, massacres and one of the world's largest refugee problems. This conflict is excellently summarized in this Reuters report. If not for your own well-being, we would encourage you to refrain from supporting violence against the Colombian people by purchasing cocaine.