Zero-Shot Object Goal Navigation enables robots to navigate toward objects of unfamiliar categories without prior training. Traditional approaches often leverage categorical semantic information for navigation guidance, which struggles when only partial objects are observed and lack detailed and functional representation of the environment. In contrast, we propose Geometric and Affordance Maps (GAMap), a novel method that integrates geometric and affordance attributes for navigation guidance. Our method includes a multi-scale scoring approach to capture geometric and affordance attributes of objects at various scales. 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 and affordance-guided navigation strategy in enhancing robot autonomy and versatility without additional training or fine-tuning on semantic knowledge or locomotion.