Sightseeing

Rambla:

The Rambla is, of course, the best known landmark of Barcelona, and deservedly so. Meandering down from the Pl. de Catalunya to the Columbus statue, filled with newspaper kiosks, flower and animal stalls, and all sorts of artists, it is undoubtedly the place where everyone comes together, both tourists and locals, from the most inconspicuous to the most exaggerated representative of all sorts of urban tribes. 
Of interest is the Miró Mosaic, the Liceu (Opera house), the Mercat de la Boqueria or exhibition centres such as the Palau de la Virreina and the Centre d'Art Santa Mònica. 
When you feel tired, have a drink at one of the many terraces, try your luck at the Café de la Ópera.
Strolling down the Rambla, on your right is the Barri del Raval, formerly known as the "barrio chino", the red-light district of the city. This area no longer has a bad reputation. In the Raval you will find many small restaurants and night bars where you can spend a very pleasant evening. 
In Calle Montalegre you'll find the Centre de Cultura Contemporània de Barcelona, which houses various exhibitions and the restored Museu d'Art Contemporani. 
Further down the Ramblas, in Calle Nou de la Rambla, is the Palau Güell, by Gaudí. You should not miss Pl. Reial, on your left, with its archway and palm trees (some say the tallest of Europe). It used to have a bad reputation, but has now become one of the safest places in the city. From this square go to Calle Ferran, which leads to Pl. Sant Jaume, where the Palau de la Generalitat and the Town Hall can be found. 
Once in the Barri Gòtic, the best thing to do is to wander round the small streets, exploring them for yourself. But don't miss the Pl. de Sant Josep Oriol, with its afternoon concerts. Pl. de Sant Felip Neri, the most romantic of the city, the Cathedral with its fine cloister, the Calle del Bisbe and the Pl. del Rei. 
If you're not too tired, it's time to go shopping around Portaferrissa and Portal de l'Àngel. 
You're not through with Ciutat Vella yet: you still have to visit the Barri de la Ribera, which is down to the right of Via Laietana, and where, among many others, you can find the Museu Picasso and the church of Santa Maria del Mar, the most representative example of the austere Catalan gothic style. This area, and that of the Pg. del Born, are rich in restaurants and bars where you can have a drink late at night.