The excessive use of digital devices such as cameras and smartphones in smart cities has produced huge data repositories that require automatic tools for efficient browsing, searching, and management. Data prioritization (DP) is a technique that produces a condensed form of the original data by analyzing its contents. Current DP studies are either concerned with data collected through stable capturing devices or focused on prioritization of data of a certain type such as surveillance, sports, or industry. This necessitates the need for DP tools that intelligently and cost-effectively prioritizes large variety of data for detecting abnormal events, and hence effectively manages them, thereby making the current smart cities greener. In this paper, we first carried out an in-depth investigation on the recent approaches and trends of DP for data of different nature, genre, and domain of two decades in green smart cities. Next, we proposed an energy-efficient DP framework by intelligent integration of Internet of things, artificial intelligence, and big data analytics. Experimental evaluation on real-world surveillance data verified the energy-efficiency and applicability of this framework in green smart cities. Finally, this article highlights the key challenges of DP, its future requirements, and propositions for integration into green smart cities.