Recent advances in Large Language Models (LLMs) have expanded their role in human interaction, yet curiosity -- a central driver of inquiry -- remains underexplored in these systems, particularly across cultural contexts. In this work, we investigate cultural variation in curiosity using Yahoo! Answers, a real-world multi-country dataset spanning diverse topics. We introduce CUEST (CUriosity Evaluation across SocieTies), an evaluation framework that measures human-model alignment in curiosity through linguistic (style), topic preference (content) analysis and grounding insights in social science constructs. Across open- and closed-source models, we find that LLMs flatten cross-cultural diversity, aligning more closely with how curiosity is expressed in Western countries. We then explore fine-tuning strategies to induce curiosity in LLMs, narrowing the human-model alignment gap by up to 50%. Finally, we demonstrate the practical value of curiosity for LLM adaptability across cultures, showing its importance for future NLP research.