Social media has become an important platform for people to express their opinions towards transportation services and infrastructure, which holds the potential for researchers to gain a deeper understanding of individuals' travel choices, for transportation operators to improve service quality, and for policymakers to regulate mobility services. A significant challenge, however, lies in the unstructured nature of social media data. In other words, textual data like social media is not labeled, and large-scale manual annotations are cost-prohibitive. In this study, we introduce a novel methodological framework utilizing Large Language Models (LLMs) to infer the mentioned travel modes from social media posts, and reason people's attitudes toward the associated travel mode, without the need for manual annotation. We compare different LLMs along with various prompting engineering methods in light of human assessment and LLM verification. We find that most social media posts manifest negative rather than positive sentiments. We thus identify the contributing factors to these negative posts and, accordingly, propose recommendations to traffic operators and policymakers.