The spatial configuration of urban amenities and the streets connecting them collectively provide the structural backbone of a city, influencing its accessibility, vitality, and ultimately the well-being of its residents. Most accessibility measures focus on the proximity of amenities in space or along transportation networks, resulting in metrics largely determined by urban density alone. These measures are unable to gauge how efficiently street networks can navigate between amenities, since they neglect the circuity component of accessibility. Existing measures also often require ad hoc modeling choices, making them less flexible for different applications and difficult to apply in cross-sectional analyses. Here we develop a simple, principled, and flexible measure to characterize the circuity of accessibility among heterogeneous amenities in a city, which we call the pairwise circuity (PC). The PC quantifies the excess travel distance incurred when using the street network to route between a pair of amenity types, summarizing both spatial and topological correlations among amenities. Measures developed using our framework exhibit significant statistical associations with a variety of urban prosperity and accessibility indicators when compared to an appropriate null model, and we find a clear separation in the PC values of cities according to development level and geographic region.