This paper examines the customers’ experience assessment with the luxury daily sailing tours in the area of the Elaphite Islands of Dubrovnik. For the purpose of this study, the influence of the entertainment opportunities, the educational opportunities, the aesthetics, and the escapism components on the customer’s experience is investigated, as well as the correlation between overall customer satisfaction and age groups of customers. The personal interview method was used for data collection. Tourists were interviewed on boats during the tours in the area of Dubrovnik Elaphite Islands, Croatia. The Pine and Gilmore experience model was used to define the main elements of their experience. The analytic hierarchy process model was used for the customers’ experience assessment. According to the results of this study, entertainment and aesthetics have greater influence than education and escapism on customer satisfaction in the age group up to 30 years. Entertainment and escapism have greater influence than education and aesthetics on customer satisfaction in the age group from 31 to 60. The interesting findings of this study are that education and aesthetics have a greater influence than entertainment and escapism for the elderly, e.g., for the customers in the age group older than 61. The highest overall satisfaction with the daily sailing tour was found among tourists in the age group up to 30 years, followed by tourists in the age group from 31 to 60 years, and the lowest satisfaction was shown by tourists who were older than 60 years. This study indicates that all the areas are important and that customer satisfaction with each component, e.g., with the entertainment, education, escapism, and aesthetic, varies according to the age group. This study also indicates that there is a correlation between the overall customer’s experience assessment of the “Elaphite Islands of Dubrovnik” daily sailing tour and customer age group.