We present a new framework for interior scene synthesis that combines a high-level relation graph representation with spatial prior neural networks. We observe that prior work on scene synthesis is divided into two camps: object-oriented approaches (which reason about the set of objects in a scene and their configurations) and space-oriented approaches (which reason about what objects occupy what regions of space). Our insight is that the object-oriented paradigm excels at high-level planning of how a room should be laid out, while the space-oriented paradigm performs well at instantiating a layout by placing objects in precise spatial configurations. With this in mind, we present PlanIT, a layout-generation framework that divides the problem into two distinct planning and instantiation phases. PlanIT represents the "plan" for a scene via a relation graph, encoding objects as nodes and spatial/semantic relationships between objects as edges. In the planning phase, it uses a deep graph convolutional generative model to synthesize relation graphs. In the instantiation phase, it uses image-based convolutional network modules to guide a search procedure that places objects into the scene in a manner consistent with the graph. By decomposing the problem in this way, PlanIT generates scenes of comparable quality to those generated by prior approaches (as judged by both people and learned classifiers), while also providing the modeling flexibility of the intermediate relationship graph representation. These graphs allow the system to support applications such as scene synthesis from a partial graph provided by a user.