The aim of this paper is to explore the Greek Generation Y cohorts’ food neophobia, intention to engage in entomophagy, self-assessed environmental concern, and intention to recommend entomophagy as an alternative to meat protein intake. Lastly, it groups participants based on the abovementioned variables. An online questionnaire applying a convenient sampling method collected data from 234 members of the Generation Y cohort. Regarding food neophobia, mean values (MVs) revealed that the statement “If I don’t like the look/appearance of a food/dish I won’t try it” was the highest rated (MV = 4.72 on a 7-point Likert scale). As to acceptance of entomophagy, the highest rated statement was “I would only try insect-based foods abroad (e.g., in the Far East)” with MV = 3.98 on a 7-point Likert scale. As to self-assessed environmental concern, the results revealed that participants answered that “I am quite interested in environmental issues, but they are not my immediate priority” (MV = 3.00 on a 5-point Likert-type scale) and they are not likely to recommend entomophagy to others (MV = 1.69 on a 5-point Likert-type scale). A K-means cluster analysis provided three clusters. Communication marketing and sustainability education are discussed to raise awareness of entomophagy and possible acceptance.