In the tourism and hospitality industry, ensuring the well-being of visitors is essential to achieving a competitive tourist destination. This objective is even more pressing in the gastronomy sector. Surprisingly, the scientific literature on this topic is scarce and relies on questionnaire surveys and interviews as a data source. After scrutinizing the 13 articles on gastronomy tourism and well-being indexed in the Web of Science or in Scopus, this study proposes two new lines of research interrelated by the concept of gastronomic image. These exploit the content shared online by consumers in order to assess subjective well-being derived from quality gastronomic experiences. The first is a framework for the customer-perceived image based on Grönroos’s service quality model, and the second is a conceptual model based on Morris’s semiotics to measure gastronomic image. Through mixed methodologies, i.e., qualitative in the first research line and quantitative in the second, the study applies the theoretical framework to Michelin-starred restaurants in two tourist regions with similar features but with different gastronomic cultures—Taiwan (Asia) and Catalonia (Europe)—using as a data source all the online travel reviews (OTRs) written in English about these restaurants shared on the TripAdvisor portal. Comparing the three categories of restaurants in both regions, the results show branding and marketing problems and significant differences in the popularity of restaurants and the satisfaction and well-being of diners. There is a positive relationship between the category of restaurants according to the number of Michelin stars and their popularity according to the number of OTRs, as well as with the satisfaction and well-being of diners, except for a 3-star restaurant that is the worst-rated. These outcomes from the demand side can be useful to stakeholders to design or improve gastronomic products and services.