The capture and analysis of diverse data is widely recognized as being vital to the design of new products and services across the digital economy. 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. By adopting a human perspective on data, we are able to chart out the complex and rich information that can inform design activities and contribute to datasets that can drive creativity support systems.