Smart cities require the utilization of advanced computing technology to address the intricate challenges posed by the rapid expansion of metropolitan areas. This study discusses the use of intelligent computing systems in smart cities, specifically emphasizing their conceptual frameworks, essential components, and actual implementations. Smart computing systems consist of several technologies, including Internet of Things (IoT) devices, artificial intelligence (AI), and big data analytics. These technologies collaborate to enhance urban infrastructure and services. The aim of this article is to provide a comprehensive understanding of how intelligent computing systems might potentially transform urban living and make substantial contributions to the progress of sustainable, efficient, and resilient smart cities. The study explores essential components, including data collection and analysis, real-time decision-making, and resource optimization through automation and predictive analytics. The article represents the framework of IoT, integration of various smart components, operation of devices, working with data collected, smart monitoring of urban infrastructures, application of smart computing aspects for smart homes and smart cities by discussing real time example. The article additionally examines the challenges and potential associated with the adoption of these technologies, including concerns over data privacy, the need for robust cyber security measures, and the importance of scalable solutions. The article represents an overall framework for further research and progress in intelligent computing systems for smart cities and infrastructures.