On the quayside at Puntarenas are plenty of taxi drivers holding boards advertising trips such as a drive to the rain forest. Or you could do what we did, ask to be taken on a drive which includes seeing the alligators, a tourist spot where there is an impressive number of the creatures, and the white-faced monkeys (capuchins) for which the area is famous. We paid US$50 for pretty much a morning in our own taxi which we thought was good value (and, of course, much cheaper than similar things done by the ship). Cartagena is a lovely city (ask for the old town) with much colonial history and buildings. In my view it is too far to walk and the route is not particularly attractive, but the city is walkable once you get there. The taxi drivers at the port operate something of a cartel which means they all want US$20 to get into town (I once agreed US$15). So just go with them one-way and when you return to the ship get a street cab (there are zillions) and you'll pay about US$5.
i would be very careful in costa rica, you may be safer to stick to the ships excursions. a few years ago my ex and i took a holiday to costa rica, we hired a car and on returning it the car hire firm claimed we had damaged it ( not true ) and demanded $600. we refused to pay and they said they would call the police, we told them too and when the police arrived they held a shotgun at my ex's head and told us too pay! obviously we did, we were at the airport with a flight to catch which they were well aware of. when we returned to new orleans where we were living, we complained to our insurance and the US police and apparantly this is commonplace, to add insult to injury the credit card we paid on was then charged with loads of fraudulent charges. i know this can happen anywhere and we were probably just unlucky, but i would be very careful there is a lot of organised crime. on the plus side once you head out of san jose ( a dump) there is lots to see and it is a very beautiful country. enjoy it, just be safe.
Thank you both so much for the information - .