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We focus on its use to inspire the co-design of visitor experiences in museums as a distinctive case that reveals opportunities and challenges for the use of personal data. We present a portfolio of data-inspired visiting experiences that emerged from a 3-year Research Through Design process. These include the overlay of virtual models on physical exhibits, a smartphone app for creating personalized tours as gifts, visualizations of emotional responses to exhibits, and the data-driven use of ideation cards. We reflect across our portfolio to articulate the diverse ways in which data can inspire design through the use of ambiguity, visualization, and inter-personalization; how data inspire co-design through the process of co-ideation, co-creation, and co-interpretation; and how its use must negotiate the challenges of privacy, ownership, and transparency. 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