Despite significant costs from retrieving and processing high-fidelity visual inputs, most multimodal vision-language systems operate at fixed fidelity levels. We introduce VOILA, a framework for Value-Of-Information-driven adaptive fidelity selection in Visual Question Answering (VQA) that optimizes what information to retrieve before model execution. Given a query, VOILA uses a two-stage pipeline: a gradient-boosted regressor estimates correctness likelihood at each fidelity from question features alone, then an isotonic calibrator refines these probabilities for reliable decision-making. The system selects the minimum-cost fidelity maximizing expected utility given predicted accuracy and retrieval costs. We evaluate VOILA across three deployment scenarios using five datasets (VQA-v2, GQA, TextVQA, LoCoMo, FloodNet) and six Vision-Language Models (VLMs) with 7B-235B parameters. VOILA consistently achieves 50-60% cost reductions while retaining 90-95% of full-resolution accuracy across diverse query types and model architectures, demonstrating that pre-retrieval fidelity selection is vital to optimize multimodal inference under resource constraints.