Parks provide important benefits to those who live near them, in the form of improved property values, health outcomes, etc.; nevertheless, measuring and understanding who lives near a park is an open research question. In particular, it is not well understood which park individuals will choose to use when given a choice among a set of nearby parks of varying sizes and at varying distances from their home. In this paper we present a park activity location choice model estimated from a passive origin-destination dataset — supplied by StreetLight Data, Inc.~— representing trips to parks and green spaces in Alameda County, California. The estimated model parameters reveal heterogeneous preferences for park size and willingness-to-travel across block-group level socioeconomic segmentation: Specifically, high-income block groups appear more positively attracted to larger parks, and block groups with a high proportion of ethnic minority individuals are more likely to select nearby parks. The findings have importance for understanding recreational access among different populations, and the methodology more generally supplies a potential template for using passive data products within travel modeling.