Don't bother with shopping in this port (the ship's suggested mall-Perrino Gallo-was a waste of time unless one is looking for emeralds, possibly). There are a few things worth buying in Cartagena (coffee, coffee candy), but the prices in the port shop were comparable to in town. Explore the city, old and new, and save the shopping for the two St.'s.
We went to Palm Beach on the bus...$2 each. A taxi ride was $15-$18 and they said the bus would never come, but we had no wait going out or coming back. Eagle beach is a bit closer and is also nice. There were places offering to rent chairs on Eagle Beach, ranging from $10 to $20 EACH. We found a resort on Palm that let us use their chairs since we were patronizing their bar. It was wonderful and relaxing...and a lot cheaper that the $125 we would have spent on a ship excursion to get us 10 miles down the shoreline.
A nice walk across the floating bridge led to some fun shopping. Prices got lower on the outskirts of the nice shopping district, but the sense of security also diminished. We found this to be a great spot to enjoy the locals and browse.
Options on this island are seemingly endless. Some say the Dutch side is best, while others prefer the French portion. We did the water taxi across the bay. It is $7 per person for unlimited rides, so one can go shopping, take their haul back to the ship and then return to enjoy the beach. There were ample options to rent chairs and a good deal can be found with a little bartering...$15-$20 for a six-pack and two chairs. There are lots of beach options on the island, but for family time we found the beaches across the bay to be great.