Large language models (LLMs) are increasingly integrated into many online services, yet they remain cost-prohibitive to deploy due to the requirement of expensive GPU instances. Prior work has addressed the high cost of LLM serving by improving the inference engine, but less attention has been given to selecting the most cost-efficient GPU type(s) for a specific LLM service. There is a large and growing landscape of GPU types and, within these options, higher cost does not always lead to increased performance. Instead, through a comprehensive investigation, we find that three key LLM service characteristics (request size, request rate, SLO) strongly influence GPU cost efficiency, and differing GPU types are most cost efficient for differing LLM service settings. As a result, the most cost-efficient allocation for a given service is typically a mix of heterogeneous GPU types. Based on this analysis, we introduce Mélange, a GPU allocation framework that navigates these diverse LLM service characteristics and heterogeneous GPU option space to automatically and efficiently derive the minimal-cost GPU allocation for a given LLM service. We formulate the GPU allocation task as a cost-aware bin packing problem where GPUs are bins and items are slices of the service workload. Our formulation's constraints account for a service's unique characteristics, allowing Mélange to be flexible to support diverse service settings and heterogeneity-aware to adapt the GPU allocation to a specific service. Compared to using only a single GPU type, Mélange reduces deployment costs by up to 77% in conversational settings, 33% in document-based settings, and 51% in a mixed setting.