As long as you take a ship's excursion and stay together, it should be OK. The hawkers will drive you crazy - they follow the tour busses everywhere. Don't buy anything from people on the street, especially perfume. You will probably find that the bottle is full of water.
Personally, I stay on the ship now. We did take an excursion to a monastery and it was very interesting, however, I can't remember the name of the tour.
I really enjoyed Cartegena when I was there in 1995 on Celebrity. Took a city tour, and then went back to the walled Old Town and walked around. Enjoyed seeing the old fort too. Enjoyed the view from the old monestary, but probably would skip that in favor of more time in the Old Town. Read Mitchner's "Caribbean" novel for the history of Cartegena before you go...it really added a lot to our visit. We saw many police and soldiers with automatic weapons. There are not nearly as many problems on the coast as in the interior of Columbia. I would recommend staying with a group tour though so you don't wander into unsafe areas in the other parts of town.
I went to Cartagena two years ago with a woman friend as part of a Panama Canal trip on Diamond.
We just walked over to the (fairly new) Visitors' Center at the pier and hired a cab. There are official cab starters and helpers.
Because I have some Spanish and was carrying a guide book, I said we didn't need a guide (they cost a little extra) but one came along for the ride anyway. Very charming fellow who had reasonably good English.
Our initiative was shopping at the Dungeons, but we also visited the fort first and, after shopping, walked around the central square. Lovely small streets surrounding it with fabulous flowering windowboxes.
The guide and driver were never far from us and came in handy for bargaining at the Dungeons. We were fortunate to get a late start and hit the Dungeons after the "cruise ship people" on tours had been through and got some terrific bargains. Thanks, of course, to our "translators" parked under a tree who seemed to be related to every vendor.
We never felt worried or threatened in any fashion. While we were wandering the central square and environs we were the only women in sight but were treated with complete respect. "The Guys" were at an outside cafe having coffee and keeping an eye on us at all times.
The guys selling postcards, etc. can be annoying. I knew enough tame Spanish insults to keep them at bay. I knew better that to use the really bad ones :o)
Bottom line, we didn't feel unsafe at all and it was a terrific day.
What you decide to do will depend, of course, on your own comfort level.
I have been to Cartagena twice, once (about 5 years ago) took the city tour already mentioned that hits the highlights, old Fort and Monastery. Nice tour, goes through lots of poverty, but that's to be expected in a city with the number of poor that Cartagena has. That tour also stopped at the Dungeons shopping already mentioned and at a nice shopping mall where "Greenfire Emeralds" Store is. I left the tour at the Mall and got Greenfire to call a cab for me when I was ready to go back to the ship. I had no problem, bought beautiful emerald earrings and a ring for my mother. I paid $6.00 US for a cab back to the port.
The second time I decided I just wanted to take a cab to the Mall with Greenfire, so I walked to the aforementioned visitors center (there were 3 of us) and tried to get a cab. They quoted me a price of $60 roundtrip for the trip I got for $6.00 3 years earlier! I refused, told them I would go back to the ship before I would pay $30 each way for a 15 min. cab ride, and after quite a bit of bargaining, we agreed to pay $10.00 each way for a total of $20. I told them they didn't have to stay with us while we shopped, but they did anyway and were very pleasant and actually took a short city tour diversion on the way back to the ship. I felt perfectly safe in the cab, but the moral of my story is agree on a price before you leave the pier!
We had a very good experience both times at Greenfire, but that's a whole other story. e-mail me if you want that one!