We adapt the classic monocentric city model to consider three main topics related to the possible widespread adoption of autonomous vehicles (AVs): sprawl, energy consumption, and housing affordability. AVs are modeled to reduce marginal commuting costs and in some cases, reduce demand for center-city and residential parking. This creates opposing forces that lead to sprawl in some models and increasing density in others. All models point to welfare increases, but also increases to energy consumption due to longer commutes, greater traffic congestion, and higher productivity, calling into question claims that autonomous vehicles will save energy. In most models, AVs lead to greater housing affordability by making suburban areas more accessible, and by reclaiming land that was previously used for parking. Effects of AVs on cities are substantial and depend on the manner in which this new technology is implemented.