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Barcelonea also has a safe and clean metro service you might try that from Las Rambles to the Nou Camp.
It's only about 7 km (4miles) so cab it. Its too far to walk to the train station.
You can take the bus,there are two routes that run continuously and you can jump on and off all day at different stops. There is a stop close to the cruise ships and it takes about an hour and a half to go round the city. Great value and a good way to see Barcelona. The Nou Camp is about the furthest stop from the ships so you get a tour thown in by default! There is a stop right outside the Nou Camp.
I'd just like to re-iterate the previous post. The open top circular bus route is the best option. The ships are generally in port for a full day so you've got plenty of time. If you're a sports enthusiast then you may want to consider going on to the Olympic Stadium. I think that it's on the same route. Then you can hop back on the bus to go back into Barcas' centre or get the cable car back down as the Olympic Stadium isn't far from it. Hope you have a good time.
We went on Ocean Village 2 last year, my 15 year old son wanted to see the Nou Camp, we went on the metro, got a shuttle from the ship, walked less than 10 mins to the station, money into a ticket machine, found the stop about 15 mins walk to the stadium, lots of people going there, very easy to find. Worst luck and dont know how many times this happens they had a power cut and were not doing any tours until it came back on, we had lunch there and waited a while but no luck, walked back to the station, no ticket machines were working because of the power cut, but they just waved you through, went back to las rambles and he enjoyed watching all the street entertainers.
The above link should help you. Use the Metro, it is clean and easy or one of the circular tour buses. Barcelona is a great city to do some walking and get the feel of the place.