Cartagena, despite its touristy first impression, is a big cultural center: there's plenty going on, from sports to theater. You may have to dig a little to find local concerts, sporting events and exhibitions, but it's all there and worth seeking out.
Cartagena's local football team, Real Cartagena, plays games at Estadio Olímpico Jaime Morón León, located 5km south of the city. Games run throughout the year. Buy tickets at the stadium. A taxi there will cost around COP$12,000.