Take this portbus:
It's 3 EUR for a return ticket.
Bus stops in front of each Terminal at Mol Adossat.
It takes you the Columbus Colomn (If your ship is smaller and calls World Trade Center - then it's walking distance).
Once you arrived here between the trees...
Go to towards the Columbus Colomn to catch the HoHo-Bus
and oppotsite site of the square... there is Drassenes-Station at Route 3:
TMB have a very great website to discover Barcelona:
And going to the waterside you'll go on the harbour cruise which is also very nice:
Two routes are available:
one goes to the inner port which allows you to make pictures of your own cruise ships...
The other goes around to Diagonales Mar area to see parts like these:
But if you like to walk from here:
you are just few blocks from Gothic Quarter:
and La Rambla
incl. La Boqueria
or you walk over to World Trade Center and get on the rope car:
to go on Miramar and Montjuic to have these views:
if you go on the right time... and at all other times:
and if you walk a little upwards you can get on the rope car from Montjuic to the Castell
http://www.tmb.cat/en_US/barcelona/moute/planols/planols.jsp (at the bottom left: Teleferic de Montjuic)
and enjoy these views
All in walking distance to Columbus Column.