A fundamental issue faced by experience providers-ranging from retail to culture-is displaying a collection of items for physical and digital interactions. The arrangement of the exhibits in different locations, which we call the layout, affects the visitors' choices over time and space, thereby driving their engagement with the offered experience. In a collaboration with the Van Gogh Museum (Netherlands), we develop a predict-then-optimize framework to inform such operational decisions. First, we propose a sequential choice model, called pathway multinomial logit, that represents visitor activity as a sequence of conditional logit outcomes influenced by the layout. Estimation on large-scale visitor activity logs recorded on multimedia guides reveals that increase in spatial distances and search distances on the multimedia guide interface are strongly correlated with a reduction of transition propensity between artworks, while also uncovering relationships with artwork characteristics and contextual features. Counterintuitively, in response to more congestion, visitors may interact with more exhibits, including less prominent artworks. Our model predicts the next visitor transition with an out-of-sample accuracy of 63\%. We test the predictive accuracy of our model against several benchmarks and modified layouts. Finally, we formulate the layout optimization problem, where the goal is to assign artworks to different locations to maximize the expected length of visitors' paths. We establish a strong inapproximability result for this new optimization setting. Our simulations suggest that optimized layouts might lift visitor engagement by and retention exerted the