The port shuttle bus drops you off near to the bottom of Las Ramblas near the Columbus monument. There is a tourist bus stop across the road. Alternatively you can walk up Las Ramblas from there.
The shuttle bus will drop you at the bottom of Las Ramblas and you can walk up there to Placa de Catalunya which is the big square at the top. The tourist bus that does the north circuit operates from there (outside El Corte Ingles dept. store) and takes in Gaudis famous church Sagrada Familia and also the Camp Nous football stadium. We did this trip and went upstairs on the bus to get the best views of the architecture...on our return to Placa de Catalunya we then walked down Las Ramblas passing the street performers and stalls on the way...back to the shuttle bus stop. I wouldn't waste your money on a ships tour. The tourist bus has a running commentary through headphones.