Inferring the unknown properties of a place relies on both its observed attributes and the characteristics of the places to which it is connected. Because place characteristics are unstructured and the metrics for place connections can be diverse, it is challenging to incorporate them in a spatial prediction task where the results could be affected by how the neighborhoods are delineated and where the true relevance among places is hard to identify. To bridge the gap, we introduce graph convolutional neural networks (GCNNs) to model places as a graph, where each place is formalized as a node, place characteristics are encoded as node features, and place connections are represented as the edges. GCNNs capture the knowledge of the relevant geographic context by optimizing the weights among graph neural network layers. A case study was designed in the Beijing metropolitan area to predict the unobserved place characteristics based on the observed properties and specific place connections. A series of comparative experiments was conducted to highlight the influence of different place connection measures on the prediction accuracy and to evaluate the predictability across different characteristic dimensions. This research enlightens the promising future of GCNNs in formalizing places for geographic knowledge representation and reasoning.