Understanding how the built environments of historic districts shape tourist experiences and behavioral intentions is important for their sustainable development. Drawing on scene theory and the Stimulus–Organism–Response (SOR) model, this study employs structural equation modeling (SEM) and fuzzy-set qualitative comparative analysis (fsQCA) to empirically analyze 498 valid questionnaire responses collected in Pingjiang Historic District, Suzhou, China. The study examines the relationships among built environmental stimuli, psychological experience, and tourist behavioral intentions. The findings show that: (1) Tourist behavioral intentions are associated with multiple interacting conditions rather than a single linear factor; (2) A distinctive cultural atmosphere and sustained cultural knowledge experiences may provide conditions that support tourists’ attachment to the district and are associated with intentions to revisit, recommend, and share their experiences. Rich sensory experiences and locally distinctive activities may contribute to hedonic experience, place attachment, and cultural identity, thereby supporting positive behavioral intentions. In addition, integrating cultural knowledge into interactions among tourists and between tourists and local groups may provide a context in which hedonic experience and positive behavioral intentions are more likely to emerge. (3) Among the psychological experience variables, strengthening tourists’ identification with local culture can provide a relatively stable psychological basis for revisiting, recommending, and sharing historic-district experiences.