Can't remember the places we stayed as were there for a few weeks so eventually treated ourselves to a self catering apartment with garage and a rooftop pool for about $30/night...
Getsemani is the area for cheap hostels, just off the square. Quite a few have courtyards where you could do maintenance etc. Don't know how up to date this info is be here it is anyway:
Budget hostels in Cartagena.
There are 3 areas to stay in: most traveler hostels are in Getsemani, a few blocks from the old town. The old town itself houses some more expensive hotels. And Bocagrande is the modern district with modern hotels but not much charm.
Hostal Casa Viena (
Hostel Hostal Cartagena Villa de Leyva Colombia for Backpacker, Getsemani, Calle San Andres No 30 - 53, tel 664 62 42 or 660 20 77, hotel at casaviena.com), run by the friendly Austrian owner Hans, Casa Viena has dorm beds (8000 pesos, US$ 3) and private rooms (25000 pesos, US$ 10), internet, safety boxes, book exchange, open kitchen and all the usuals of a good travelers hostal. Hans can also help you get on a sailboat trip to Panama.
Hotel Marlin (Calle 30 No 10 - 35, tel 664 35 07) is a small backpackers place. Singles are 16000 pesos (US$ 6), doubles 28000 (US$ 13).
Hotel Holiday (Calle de la Media Luna No 10 - 47, tel 664 09 48) is a good option when Casa Viena is full. Singles with bathroom are 12000, doubles are 24000 pesos (US$ 10).