This study is based on the assertion that science museums should consider visitors' views and expectations as they are not satisfied in many cases. In this study, we investigated 31 scientifically gifted students and 177 science high school students about their image of science museums. Using the questionnaire, it was found that only 51% of students visited science museums; however, the average number of visits was 4.2. This means that students tended to re-visit after the first visit of the science museum. Students had a 'good' image of science museums when they incurred hands-on experiences and observed new, interesting, curious and funny exhibits. And students had a 'bad' image of science museums due to the following aspects: lack of new and interesting exhibits, information and guide, diverse contents, and hands-on experience; deficiencies in environment; and inadequacy of the management, operation and composition of exhibits. Therefore, they hoped that science museums will provide more hands-on experiences and experiments, new and interesting exhibits, systematic management and composition of exhibits, information and guides, and a good environment. So science museums need to pay special attention to aspects like management, information guides and environment for the first-time visitors. Based on the above results, we suggested "Directions for a good science museum based on students' views." While asking students what topics they wanted to know and learn in a science museum, each student was given the choice of four topics; eventually, 2.9 answers overlapped for each topic. When classifying students' topics into four main themes for the Gwangju National Science Museum, the order from the most popular theme to the least one was 'science in everyday life', 'ocean/space/future science', 'light and science', and 'culture, art and science.' Among the topics mentioned by students, only 37% are exhibited in Seoul, Gwacheon, Daejeon, or Gwangju science museums. We hope that the results and research methods will be used for evaluation, re-construction, and reinvigorated presentation of science museums.