Bit of a transport cheat but it is a something you need to go to when in Cartagena. At the moment it is on the 'Port' but they say it will soon be moved to protect it from the elements.
I will not bore you with it's history but it is interesting and something of a surprise.
No car and you are in Cartagena then take the train to the coast of the Mar Menor to Los Nietos.
This narrow gauge railway takes in various stops on the way and is a good way to reach the Mines of La Union where the station is a short walk from the attraction.
Cartagena to Los Nietos on the Mar Menor takes about 1/2 an hour.
Cartagena Feve station is just across the road in a 'lovely' yellow building.
Try La Viva restaurant on the beach at the very end of the line!!!!
Yes, Murcia is the closest airport to Cartagena and Ryanair do cheap flights between Dublin and Murcia. DUB -> MJV
I would definitely recommend renting a car if coming to Cartagena. There is public transport, but car hire is cheap and you will make much more of your journey with one. You can hire at the airport. Have a look online to compare deals. I live here, but found goldstar the cheapest when I look for guests staying.
Hope this helps!
We tried to take a train to Grenada. Wasn't happening. Only runs we could find were up to Madrid then back down. So we went to the bus station where I broke the golden rule of busses and got on a bus with a TV. It was ofcourse in Spanish but still fun to watch as the scenary rolled by outside.