Articulated object manipulation is a fundamental yet challenging task in robotics. Due to significant geometric and semantic variations across object categories, previous manipulation models struggle to generalize to novel categories. Few-shot learning is a promising solution for alleviating this issue by allowing robots to perform a few interactions with unseen objects. However, extant approaches often necessitate costly and inefficient test-time interactions with each unseen instance. Recognizing this limitation, we observe that despite their distinct shapes, different categories often share similar local geometries essential for manipulation, such as pullable handles and graspable edges - a factor typically underutilized in previous few-shot learning works. To harness this commonality, we introduce 'Where2Explore', an affordance learning framework that effectively explores novel categories with minimal interactions on a limited number of instances. Our framework explicitly estimates the geometric similarity across different categories, identifying local areas that differ from shapes in the training categories for efficient exploration while concurrently transferring affordance knowledge to similar parts of the objects. Extensive experiments in simulated and real-world environments demonstrate our framework's capacity for efficient few-shot exploration and generalization.