Urbanization has intensified traffic loads, posing significant challenges to the efficiency and stability of urban road networks. Overloaded nodes risk congestion, thus making accurate intersection importance classification essential for resource optimization. This study proposes a hybrid clustering method that combines Self-Organizing Maps (SOMs), K-Means, and the Gaussian Mixture Model (GMM), which is supported by the Traffic Flow–Network Topology–Social Economy (TNS) evaluation framework. This framework integrates three dimensions—traffic flow, road network topology, and socio-economic features—capturing six key indicators: intersection saturation, traffic flow balance, mileage coverage, capacity, betweenness efficiency, and node activity. The SOMs method determines the optimal k value and centroids for K-Means, while GMM validates the cluster membership probabilities. The proposed model achieved a silhouette coefficient of 0.737, a Davies–Bouldin index of 1.003, and a Calinski–Harabasz index of 57.688, with the silhouette coefficient improving by 78.1% over SOMs alone, 65.2% over K-Means, and 11.5% over SOM-K-Means, thus demonstrating high robustness. The intersection importance ranking was conducted using the Mahalanobis distance method, and it was validated on 40 intersections within the road network of Zibo City. By comparing the importance rankings across static, off-peak, morning peak, and evening peak periods, a dynamic ranking approach is proposed. This method provides a robust basis for optimizing resource allocation and traffic management at urban intersections.