Zero-Shot Object Goal Navigation (ZS-OGN) enables robots to navigate toward objects of unseen categories without prior training. Traditional approaches often leverage categorical semantic information for navigation guidance, which struggles when only partial objects are observed or detailed and functional representations of the environment are lacking. To resolve the above two issues, we propose \textit{Geometric-part and Affordance Maps} (GAMap), a novel method that integrates object parts and affordance attributes for navigation guidance. Our method includes a multi-scale scoring approach to capture geometric-part and affordance attributes of objects at different scales. Comprehensive experiments conducted on the HM3D and Gibson benchmark datasets demonstrate improvements in Success Rates and Success weighted by Path Length, underscoring the efficacy of our geometric-part and affordance-guided navigation approach in enhancing robot autonomy and versatility, without any additional task-specific training or fine-tuning with the semantics of unseen objects and/or the locomotions of the robot.