There are certain pictures that everyone takes when they travel: the Eiffel Tower, the Brooklyn Bridge, Big Ben. Such well-known landmarks are irresistible, but even with perfect technical skills, the best you can hope for is a postcard-perfect shot—a shot taken a millions times before.
To get a unique shot of an over photographed place, shoot the landmark when something interesting is happening. Most major cities around the world hold many festivals, parades, races, etc. Plan your visit to coincide with the beer festival in Brussels, for example or the New York Marathon, and not only will you have a lot more photo opportunities in general, but you can get shots of famous landmarks that tell a story. (London Marathon passing Big Ben photo via BBC, New York Marathon on Verrazano Bridge via nyc.gov)