Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to significantly improve safety and transportation efficiency by monitoring transportation network conditions and making better operating decisions. CAVs, however, could alter tendency-to-travel, which would eventually lead to a high traffic demand causing rebound effects (e.g., increasing vehicle miles traveled). In this paper, we focus on the social factors that could drive an emerging mobility system with CAVs to unsustainable congestion levels. We propose a mobility market to model the travelers' decision-making on how to travel in a smart city network with connected roads and public transit infrastructure. Using techniques from mechanism design, we introduce appropriate monetary incentives (e.g., tolls, fees, subsidies), and we show how a mobility system consisting of selfish travelers that seek to travel either with a CAV or use public transit can be socially efficient. We prove that our mobility market is incentive compatible, individually rational, and weakly budget balanced. Thus, our mobility market ensures that travelers always report their personal travel requirements truthfully, always benefit from participating in the market, and the market always generates revenue from each traveler.