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Sleep is essential for learning and cognition, but the mechanisms by which it stabilizes learning, supports creativity, and manages the energy consumption of networks engaged in post-sleep task have not been yet modelled. During sleep, the brain cycles between non-rapid eye movement (NREM), a mainly unconscious state characterized by collective oscillations, and rapid eye movement (REM), associated with the integrated experience of dreaming. We propose a biologically grounded two-area thalamo-cortical plastic spiking neural network model and investigate the role of NREM - REM cycles on its awake performance. We demonstrate that sleep has a positive effect on energy consumption and cognitive performance during the post-sleep awake classification task of handwritten digits. NREM and REM simulated dynamics modify the synaptic structure into a sharper representation of training experiences. Sleep-induced synaptic modifications reduce firing rates and synaptic activity without reducing cognitive performance. Also, it creates novel multi-area associations. The model leverages the apical amplification, isolation and drive experimentally grounded principles and the combination of contextual and perceptual information. In summary, the main novelty is the proposal of a multi-area plastic model that also expresses REM and integrates information during a plastic dream-like state, with cognitive and energetic benefits during post-sleep awake classification.