Cities host diverse people and their mixing is the engine of prosperity. In
turn, segregation and inequalities are common features of most cities and
locations that enable the meeting of people with different socio-economic
status are key for urban inclusion. In this study, we adopt the concept of
economic complexity to quantify the ability of locations -- on the level of
neighborhoods and amenities -- to attract diverse visitors from various
socio-economic backgrounds across the city. We construct the measures of
neighborhood complexity and amenity complexity based on the local portfolio of
diverse and non-ubiquitous amenities in Budapest, Hungary. Socio-economic
mixing at visited third places is investigated by tracing the daily mobility of
individuals and by characterizing their status by the real-estate price of
their home locations. Results suggest that measures of ubiquity and diversity
of amenities do not, but neighborhood complexity and amenity complexity are
correlated with the urban centrality of locations. Urban centrality is a strong
predictor of socio-economic mixing, but both neighborhood complexity and
amenity complexity add further explanatory power to our models. Our work
combines urban mobility data with economic complexity thinking to show that the
diversity of non-ubiquitous amenities, central locations, and the potentials
for socio-economic mixing are interrelated