We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.