We have no way of really knowing what difference the presence of the royal family makes to tourism figures. There have been countless polls and most of them come up with different conclusions. However, if you are inclined to believe statistics, there's an article in the Independent today reporting that a recent US poll demonstrates that if the UK were to become a republic it would not affect Americans' decision to come here on holiday.
I think it's a shame we talk this country down by implying that the only thing it's got going for it is a royal family. We have a wonderful capital city, which has a large amount of green space and beautiful museums, as well as many interesting, vibrant and different cities throughout the UK, AND beautiful and varied countryside - The Yorkshire dales, the Scottish highlands, the Cornish coast, Dartmoor, Exmoor, the Sussex downs, the Lake district, the Welsh valleys, to name but a few.
As for the royal family being "good value", the official estimated annual cost is £38.3m, but once "hidden" costs are included (such as round-the-clock security, lavish overseas visits and travel arrangements, the lost revenue from the Duchy of Cornwall - how can we justify Prince Charles owning most of Cornwall)?, it's estimated that the actual cost is more like £202.4m. Anyway, we'll never know because the monarchy's finances are exempt from the scrutiny of the Freedom of Information Act.