By the end of 2020, a total of 34 multifunctional Assistive Technology Resources Centers (ATR centers) were set up in 22 counties and cities in Taiwan. This study examines the perceptions of the users and their caregivers of the government-established ATR centers in Taiwan and examines the impact on the reputation of the public institution. The research framework and hypotheses were developed by examining the factors of “service convenience”, “center-related factors”, “justice”, and “perceived value” and using “perceived value” as a mediating variable. The data were collected through a questionnaire survey, and the structural equation model was used to test the model and verify the hypotheses. Research data was collected in various townships in Yunlin County A total of 320 questionnaires were collected. Of these respondents, 22% were aged 51–60. All the research hypotheses were positively and significantly verified. Of these, justice was the most important factor affecting the value of the ATR center’s services compared to convenience and center-related factors. Of convenience, service value and justice, service value was the most important factor affecting the perceived reputation of the public institution. According to the findings of this study, it is beyond expectation that the convenience of ATR is not the main factor influencing the service value, but rather the perceived justice is the most important factor. Therefore, ATR should be prioritized from the perspective of the service recipient, especially the perceived justice of the service, in order to best enhance the value of the service and improve the reputation of the public institution.