Definitely Sagrada Famillia (go on a Sunday morning)
Olympic Village (walk along seafront)
Harbour and Port Vell
Las Ramblas (great at any time)
cable car across the harbour to Montjuic (explore the mountain and all of the attractions there)
the quaint fishing village of Barceloneta
Parc Guell (described as being like a surreal Disneyland)
Exiemple (suburb full of Modernista architecture)
Joan Miro sculpture
Barcelona Cathedral in the Barri Gotic.
Camp Nou football ground (do the stadium tour)
El Born and Barri Gotic (especially at night)
Parc de la Ciutadella (great for Sunday afternoon strolls)
FURTHER AFIELD:
Go up to Tibidabo on a clear day (there are also some theme park attractions up there)
Montserrat on a clear day
Sitges (vibrant and authentic seaside resort)
SHOPPING LOCATIONS:
All along Las Ramblas, side streets off Las Ramblas, around the Port Vell, Placa de Catalunya, Passeig de Gracia, in the Exiemple west of Passeig de Gracia (explore the side streets) El Corte Ingles (splendid department store in Place de Catalunya for all of your needs, including a supermarket in the basement).
BEACHES:
The best ones are on a stretch of urban coastline between Barceloneta and Parc del Mar, including the Olympic Village and Poble Nou.
RESTAURANTS:
There is a lovely al fresco one in the Port Vell, just after the aquarium and just before the entrance to Maremagnum shopping centre.
BEST WAY OF GETTING AROUND:
Walk, get the metro (cheap and efficient)
Get the cable car from the harbour to Montjuic.
Get the airport bus from the terminal to Placa de Catalunya (around