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Scientific studies investigating laws and regularities of human behavior are nowadays increasingly relying on the wealth of widely available digital information produced by human activity. In this paper we use big data created by three different aspects of this activity (i.e., Bank card transactions, geotagged photographs and tweets) in Spain for quantifying city attractiveness for foreign visitors. An important finding of this paper is a strong super linear scaling law of city attractiveness with its population size. The observed scaling exponent stays nearly the same for different ways of defining cities and for different data sources, emphasizing the robustness of our finding. We also consider temporal variation of the scaling exponent in order to reveal seasonal patterns in the attractiveness. Finally, we propose a possible explanatory mechanism for the observed super linear effect based on a simple discrete choice model.