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Use Kings Cross' Clink78 or Clink261 hostels in the former red light district as your base. Attractions nearby include Bloomsbury's many squares, the British Library and British Museum.
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Camden is a short walk north, through St. Pancras Gardens and Royal College Street. Arts and crafts, superb independent stores and coffee shops are some of the attractions of this unusual neighbourhood. Wander through the markets and lose yourself in this über-trendy maze. Time it so you that can stop in the authentic Italian Casa Tua on your way in or out, and avoid those food stalls offering iffy tasters to passers by.
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A free walking tour is another brilliant idea for discovering this dazzling city on foot. The freetoursoflondon.com crew meets every day at 11 a.m. by Churchill's statue in Parliament Square. It lasts 2.5 hours, and advanced booking is not necessary. The guides work on a 'pay-what-it's-worth' basis and are enthusiastic storytellers, regaling walkers with tales about Big Ben, Buckingham Palace and Trafalgar Square.
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The well-kept lakeside lawns of St. James's Park are a great spot to take a break in the busy city centre. Food in this royal park, steps from Buckingham Palace, is very expensive so pack a lunch. The big supermarket chains - Tesco and Sainsbury's - have convenience stores at the main stations. Otherwise, stuff your backpack with goodies from a traditional English corner shop.
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Up from Trafalgar Square at the end of the park, behind the National Gallery (free admission), is Leicester Square with a dozen cinemas. With some luck, you'll catch a glimpse of a Hollywood star smiling for the cameras at yet another film premiere. Head towards Piccadilly Circus nearby and take in the famous giant neon signs and video displays.
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For a quick, tasty and reasonably-priced meal, walk up Regent Street, cross Oxford Circus, and get a divine burrito at Tortilla, just off Oxford Street in Market Place. Select the fillings for your wrap at the counter including veggie and carb-free options.
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Going out in London is an expensive undertaking. The drinks are extremely overpriced in the packed pubs and bars around town, and the clubs charge a fortune at the door. The traditional gay venues are not any different. A way around the extortion is to look for student parties, advertised on flyers around the University of London in Russell Square.
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Or buy drinks from the corner shop and head to a park nearby. With extended opening hours into the summer evenings, the chances are that other groups of equally friendly people will be doing exactly the same thing.