In open-vocabulary mobile manipulation (OVMM), task success often hinges on the selection of an appropriate base placement for the robot. Existing approaches typically navigate to proximity-based regions without considering affordances, resulting in frequent manipulation failures. We propose Affordance-Guided Coarse-to-Fine Exploration, a zero-shot framework for base placement that integrates semantic understanding from vision-language models (VLMs) with geometric feasibility through an iterative optimization process. Our method constructs cross-modal representations, namely Affordance RGB and Obstacle Map+, to align semantics with spatial context. This enables reasoning that extends beyond the egocentric limitations of RGB perception. To ensure interaction is guided by task-relevant affordances, we leverage coarse semantic priors from VLMs to guide the search toward task-relevant regions and refine placements with geometric constraints, thereby reducing the risk of convergence to local optima. Evaluated on five diverse open-vocabulary mobile manipulation tasks, our system achieves an 85% success rate, significantly outperforming classical geometric planners and VLM-based methods. This demonstrates the promise of affordance-aware and multimodal reasoning for generalizable, instruction-conditioned planning in OVMM.