Nano-optic imagers that modulate light at sub-wavelength scales could enable new applications in diverse domains ranging from robotics to medicine. Although metasurface optics offer a path to such ultra-small imagers, existing methods have achieved image quality far worse than bulky refractive alternatives, fundamentally limited by aberrations at large apertures and low f-numbers. In this work, we close this performance gap by introducing a neural nano-optics imager. We devise a fully differentiable learning framework that learns a metasurface physical structure in conjunction with a neural feature-based image reconstruction algorithm. Experimentally validating the proposed method, we achieve an order of magnitude lower reconstruction error than existing approaches. As such, we present a high-quality, nano-optic imager that combines the widest field-of-view for full-color metasurface operation while simultaneously achieving the largest demonstrated aperture of 0.5 mm at an f-number of 2.