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The beach of Sant Miquel just at the end of the area of Barceloneta (and often called Barceloneta Beach), is one of the famous beaches of Barcelona. Sure, many tourists are going to this beach in the summer, and in the middle of the afternoon it's really full and difficult to find a place... But if you go there early in the morning (8.00 am or after 7.00 pm) or in the late afternoon, you'll have the beach almost for you alone :).
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The hill and castle of Montjuic is really a place to see in Barcelona and a place where you can see the whole city with a unique point of view. Dominating the south-west part of the city you have the whole panorama over it on one side, and on the other side you see the great industrial installations of the port of Barcelona. Climbing up the hill is also very interesting because of the park of Montjuic and the Olympic installations from de Olympic Games 1992 (and specially the Olympic swimming and diving pool... do you remember the diving sessions where the athletes jump in the air with the background of whole BCN and the Sagarada Familia?).