We were in both places in March.
In Limon, the favorite shore excursions hands down was the white water rafting, which we unfortunately didn't take, because we live in Colorado and do that every year here. We did the rainforest hike, which was ok, but I couldn't really recommend it. No matter what you do, you will have at least an hour or so bus ride to get to it. In Puerto Limon, there is a little market place within walking distance of the ship, but the town really doesn't have enough to keep you occupied for a whole day.
In Cartagena, we rented a taxi (along with an interpreter) and saw the major city sites (a monastery, a cathedral, the fortress area). It did not appear to us to be as dangerous as people made it out to be, but, as is typical in that part of the world, there is a lot of poverty. We felt safe doing what we did, and it was very inexpensive. A lot of people bought emeralds in Cartagena, but I would not know quality when I saw it, and so stayed away from any large purchases. Also at that port terminal, there is some very minor shopping, and a good phone/internet cafe. I would not recommend just going out on your own walking beyond the port area.
If you get a chance, read at least the chapter on Cartagena from Michener's book 'Caribbean'. It gives a fascinating account of how the city's topography formed a natural defense against invaders, and as you sail in and out of port, you can see where they had strung a chain from one side to the other to prevent invaders from sailing in. Neat stuff!