In this paper, we study a wireless access network based on the Institute of Electrical and Electronics Engineers 802.11 standard and enriched with features such as caching and mesh networking. This system is analysed in terms of energy efficiency and traffic offloading, two objectives that are somewhat in contrast but both relevant to network and service providers as they directly impact the operational cost. In addition, QoS is also accounted for in the form of guaranteed bandwidth and bounded delay. To this aim, we developed a mathematical model of the system and solved it to optimality by means of integer linear programming. We can thus show how much can be saved both in terms of energy and traffic, also considering various tradeoff points among the two contrasting objectives. As a last step, we provide an investigation on the benefits of adding traffic aggregation features to the mathematical model