One of the fun outings you can do here is go see the Castillo de San Felipe de Barajas, a fortress built in the 17th and 18th centuries to protect the Spanish from invasions, and it's one fort that has never been overtaken. By this time in the trip friend and coworker Beau had joined me so we checked it out together.
Another fun thing to do in Cartagena is have dinner or a drink on "the wall." It may not look like anything special...
Travel in Colombia, especially Cartagena, is more expensive than most South American countries, so budget appropriately. Of course you can save some money if you have the luxury of coming in the off season.
In or near the walled city, if possible. I stayed part of the time at El Viajero Hostel, which I can recommend, especially for their private rooms. They have a great location. I also spent a few nights with a friend at Sonesta Hotel. The hotel was very nice, but it wasn't in walking distance to ANYTHING so anytime we wanted to go into town, get a meal, or have a drink it meant a cab ride somewhere. Not ideal unless you plan on renting a car.