Agglomeration economies drive urban growth at different spatial scales by enabling productivity gains, knowledge spillovers, and shared inputs among proximate firms and amenities. To develop a unified science of cities it is thus important to understand how and to what extent different amenities cluster or mix across scales and regional contexts. By utilizing a novel Bayesian framework for nonparametrically quantifying the spectrum of possible mixing patterns of amenities in a city, we identify universal spatial scales of homophily (agglomeration) and heterophily (co-agglomeration) among different amenity types across roughly 800 cities worldwide. Through a detailed longitudinal case study, we also find that the changes in heterophilic mixing derived from our methodology more effectively predict changes in neighborhood rental values than the diversity of amenities present. These findings suggest that agglomeration economies exhibit universal spatial regularities that depend largely on the types of firms or amenities being considered, rather than their specifics or regional context, and highlight the benefit of heterophilic amenity mixing at walkable spatial scales.