We introduce RHYTHM (Reasoning with Hierarchical Temporal Tokenization for Human Mobility), a framework that leverages LLMs as spatio-temporal predictors and trajectory reasoners. RHYTHM partitions trajectories into daily segments encoded as discrete tokens with hierarchical attention, capturing both daily and weekly dependencies while substantially reducing sequence length. Token representations are enriched with pre-computed prompt embeddings via a frozen LLM, enhancing the model's ability to capture complex interdependencies without extensive computational overhead. By freezing the LLM backbone, RHYTHM achieves significant computational efficiency. Evaluation on three real-world datasets demonstrates a 2.4% improvement in accuracy, 5.0% increase on weekends, and 24.6% reduction in training time compared to state-of-the-art methods.