We introduce Agent4POI, the first POI recommendation framework that generates context-conditioned multimodal representations at recommendation time, rather than relying on static POI embeddings pre-computed independently of context. Existing multimodal systems encode each POI once as a static embedding, a design that precludes reasoning about why the same cafe affords solo work on Monday but group celebration on Friday evening. We formally prove that no pre-computed encoder can satisfy context-sensitive ranking under standard bilinear scoring, motivating inference-time item-side representation. Agent4POI inverts this computation: given a situational context, a four-phase LLM agent generates dynamic, context-specific affordance queries (Phase 1) and executes a five-step cross-modal chain-of-thought over image, review, and metadata evidence (Phase 2). The resulting uncertainty-aware affordance representation is grounded in Gibsonian affordance theory. These cross-modal verdicts form a structured, uncertainty-adjusted affordance representation (Phase 3), which is aligned with user preferences via a semantic caching system for low-latency ranking (Phase 4). On three POI benchmarks and three evaluation configurations (standard, cold-start, context-shift), Agent4POI achieves a 23.2% relative gain over the strongest baseline and degrades by only 7.5% under context-shift versus 16--17\% for the strongest baselines. In cold-start scenarios, Agent4POI outperforms the best content-based baseline by up to 2.4x, whereas ID-based methods fail to generalize.