Routing problems are common in mobile robotics, encompassing tasks such as inspection, surveillance, and coverage. Depending on the objective and constraints, these problems often reduce to variants of the Traveling Salesman Problem (TSP), with solutions traditionally derived by translating high-level objectives into an optimization formulation and using modern solvers to arrive at a solution. Here, we explore the potential of Large Language Models (LLMs) to replace the entire pipeline from tasks described in natural language to the generation of robot routes. We systematically investigate the performance of LLMs in robot routing by constructing a dataset with 80 unique robot routing problems across 8 variants in both single and multi-robot settings. We evaluate LLMs through three frameworks: single attempt, self-debugging, and self-debugging with self-verification and various contexts, including mathematical formulations, pseudo-code, and related research papers. Our findings reveal that both self-debugging and self-verification enhance success rates without significantly lowering the optimality gap. We observe context-sensitive behavior - providing mathematical formulations as context decreases the optimality gap but significantly decreases success rates and providing pseudo-code and related research papers as context does not consistently improve success rates or decrease the optimality gap. We identify key challenges and propose future directions to enhance LLM performance in solving robot routing problems. Our source code is available on the project website: https://sites.google.com/view/words-to-routes/.