Q: Does the Aerobus service from BCN airport go anywhere near the cruise terminal? If not can you suggest a reasonably priced way of doing the journey.
A: The Aerobus (Express bus service from Barcelona Airport) will take you as far as Plaça Catalunya square in Barcelona city centre which is at the top most part of Las Ramblas. This is about 1.2km away from the Cruise port terminals.
From Plaça Catalunya you can take the underground metro station at Catalunya to Drassanes station (only 2 stops on the green line metro L3). From Drassanes metro you only have a few minutes walk to the Columbus Monuments and Port Vell. From there you can catch the T3 PORTBUS which is a shuttle bus that runs from the Columbus monument to all terminals in the cruise port. This is probably the most economical way to travel to the Cruise port if you want to use the Aerobus.
Here are some more detailed information pages that can help you plan your route: