Next location prediction is a critical task in human mobility analysis and serves as a foundation for various downstream applications. Existing methods typically rely on discrete IDs to represent locations, which inherently overlook spatial relationships and cannot generalize across cities. In this paper, we propose NextLocLLM, which leverages the advantages of large language models (LLMs) in processing natural language descriptions and their strong generalization capabilities for next location prediction. Specifically, instead of using IDs, NextLocLLM encodes locations based on continuous spatial coordinates to better model spatial relationships. These coordinates are further normalized to enable robust cross-city generalization. Another highlight of NextlocLLM is its LLM-enhanced POI embeddings. It utilizes LLMs' ability to encode each POI category's natural language description into embeddings. These embeddings are then integrated via nonlinear projections to form this LLM-enhanced POI embeddings, effectively capturing locations' functional attributes. Furthermore, task and data prompt prefix, together with trajectory embeddings, are incorporated as input for partly-frozen LLM backbone. NextLocLLM further introduces prediction retrieval module to ensure structural consistency in prediction. Experiments show that NextLocLLM outperforms existing models in next location prediction, excelling in both supervised and zero-shot settings.