The advent of broadband and tunable acoustic metamaterials, amenable to be fabricated into flat panel geometry, offers broad, emerging possibilities for room acoustics. In particular, the fine tuning of surface acoustic impedance becomes possible to optimize specific room acoustic goals. In this initial simulation study we examine the possibility of minimizing the averaged level of energy density (${L}_{e}$), both globally and locally in an enclosed room. The relationship curve between surface impedance and global ${L}_{e}$ shows an optimal value that can reduce ${L}_{e}$ by about $15$--$20\phantom{\rule{0.2em}{0ex}}\mathrm{dB}$ over a wide audible frequency regime. Moreover, partial coverage of the room surface by the optimally tuned acoustic metamaterial already demonstrates considerable effectiveness. We compare and verify our numerical model with the statistical-diffusive acoustics model and find good agreement in the high-frequency regime. In the low-frequency regime, the energy inhomogeneity caused by wave interference can be utilized to create a quiet zone for specific targeted frequency by optimally tuning the surface impedance values at discretized locations on the four walls.