With the evolution of the Internet of Things (IoT), smart cities have become the mainstream of urbanization. IoT networks allow distributed smart devices to collect and process data within smart city infrastructure using an open channel, the Internet. Thus, challenges such as centralization, security, privacy (e.g., performing data poisoning and inference attacks), transparency, scalability, and verifiability limits faster adaptations of smart cities. Motivated by the aforementioned discussions, we present a Privacy-Preserving and Secure Framework (PPSF) for IoT-driven smart cities. The proposed PPSF is based on two key mechanisms: a two-level privacy scheme and an intrusion detection scheme. First, in a two-level privacy scheme, a blockchain module is designed to securely transmit the IoT data and Principal Component Analysis (PCA) technique is applied to transform raw IoT information into a new shape. In the intrusion detection scheme, a Gradient Boosting Anomaly Detector (GBAD) is applied for training and evaluating the proposed two-level privacy scheme based on two IoT network datasets, namely ToN-IoT and BoT-IoT. We also suggest a blockchain-InterPlanetary File System (IPFS) integrated Fog-Cloud architecture to deploy the proposed PPSF framework. Experimental results demonstrate the superiority of the PPSF framework over some recent approaches in blockchain and non-blockchain systems.