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You could try Locanto for Cartagena, which has free ads posted by both owners and agencies.聽 Look under INMOBILIARIA for apartments, rooms and houses for rent:

I'd also try AirBnB and see if you can negotiate long-term rentals:

But since Cartagena is a tourist destination, you can expect prices to be high unless you really dig deep.聽 Your best bet would be to walk around and talk to people - the inhabitants are not paying vacation prices, but if you're a foreigner and staying for only a few months, it's going to be tough.

You can also do a search for

colombia cartagena apartamento arriendo

...and get many hits in Spanish for rental units.