Because of the current problems of cultural and creative tourism in tourism destination management under the cultural theory perspective, this paper aims to explore the new development direction of cultural and creative tourism. This paper uses the gray-scale correlation method model to construct a correlation degree model, analyze the factors tourists consider in choosing tourist destinations, determine the weights of each influencing factor, and extract the main influencing factors. On this basis, combined with a questionnaire survey method, we analyze the market demand for cultural and creative tourism, tourists’ satisfaction, and the existing problems of the cultural and creative tourism market and put forward suggestions for the problems. In terms of market demand, the highest percentage of tourists’ motivation for tourism is to experience different cultures 60.55%, followed by relaxation 57.35% and appreciation of scenery 55.4%, which shows that the cultural tourism market has great potential; however, there are still many problems in the current cultural tourism, the most prominent being excessive commercialization and loss of cultural authenticity, which accounts for 75%, followed by high ticket prices, lack of creativity in products, however, the service level needs to be improved to 40%, indicating that all these problems need to be paid attention to. Cultural and creative tourism is a form of tourism preferred by tourists, and many problems still need to be further explored.