Right inside the Walled City as you enter through the Clock Tower, directly above the Portal de los Dulces where the traditional candy vendors set up. Climb all four floors to the rooftop and the view that greets you is genuinely spectacular: the Clock Tower below you, Plaza de los Coches spread out beneath that, the Convention Center and Four Seasons across the bay, the Muelle de los Pegasos, and Cartagena Bay with boats coming and going. At night, with the city lit up and a breeze hitting you from above the walls, it's one of the best places to have a drink in Cartagena. It's touristy, yes. Go anyway.
The bar spans multiple levels with an indoor section on the lower floors if the rooftop fills up or the heat becomes a factor. The rooftop is open air but sits high enough that there's usually a good breeze, more so than you'd feel down in the streets. Drinks are solid. Order a glass of Dictador rum while you're there. You're in Cartagena. It would be wrong not to.