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To some extent the Royal Family does contribute to tourism, attractions like the Changing of the Guard for instance wouldn't exist without it, and the Royal Wedding drew huge amounts of worldwide interest, especially in America and Germany. But I'm not sure the tourism industry would suffer as much as people make out, because we still have plenty of other attractions like Shaun mentioned and Buckingham palace could probably still be a point of interest even without the Queen.

In principle I'm against the Monarchy but in practice I'm pretty indifferent, they don't do all that much these days and it isn't hugely costly to the taxpayer either so I find it something hard to care about