Owing to the fluctuant renewable generation and power demand, the energy surplus or deficit in each nanogrid is embodied differently across time. To stimulate local renewable energy consumption and minimize the long-term energy cost, some issues still remain to be explored: when and how the energy demand and bidirectional trading prices are scheduled considering personal comfort preferences and environmental factors. For this purpose, the demand response and two-way pricing problems concurrently for nanogrids and a public monitoring entity (PME) are studied with exploiting the large potential thermal elastic ability of heating, ventilation and air-conditioning (HVAC) units. Different from nanogrids, in terms of minimizing time-average costs, PME aims to set reasonable prices and optimize profits by trading with nanogrids and the main grid bi-directionally. In particular, such bilevel energy management problem is formulated as a stochastic form in a long-term horizon. Since there are uncertain system parameters, time-coupled queue constraints and the interplay of bilevel decision-making, it is challenging to solve the formulated problems. To this end, we derive a form of relaxation based on Lyapunov optimization technique to make the energy management problem tractable without forecasting the related system parameters. The transaction between nanogrids and PME is captured by a one-leader and multi-follower Stackelberg game framework. Then, theoretical analysis of the existence and uniqueness of Stackelberg equilibrium (SE) is developed based on the proposed game property. Following that, we devise an optimization algorithm to reach the SE with less information exchange. Numerical experiments validate the effectiveness of the proposed approach.