This paper proposes SST-iTransformer, a novel methodology for predicting parking availability by integrating demand characteristics of various transportation modes (subway, bus, online taxi-hailing, and regular taxis) to address urban parking challenges. We use K-means clustering to define parking cluster zones (PCZs) and improve upon the existing iTransformer by introducing a dual-branch attention mechanism that incorporates mask-reconstruction-based self-supervised learning, series attention to capture time-series dependencies, and channel attention to model interactions between variables. Experimental results using real-world data from Chengdu, China, demonstrate that SST-iTransformer outperforms existing deep learning models (Informer, Autoformer, Crossformer, and iTransformer), achieving the lowest MSE and competitive MAE. Furthermore, we quantitatively analyze the relative importance of various data sources, demonstrating that taxi-hailing data yields the greatest performance improvement and confirming the importance of modeling spatial dependencies.