The paper deals with modeling the cost of energy consumed in public buildings by leveraging three machine learning methods: artificial neural networks, CART, and random forest regression trees. Energy consumption is one of the major issues in global and national policies, therefore scientific efforts in creating prediction models of energy consumption and cost are highly important. One of the largest energy consumers in every state is its public sector, consisting of educational, health, public administration, military, and other types of public buildings. Recent technologies based on sensor networks and Big data platforms enable collection of large amounts of data that could be used to analyze energy consumption and cost. A real data from Croatian public sector is used in this paper including a large number of constructional, energetic, occupational, climate and other attributes. The algorithms for data pre-processing and modeling by optimizing parameters are suggested. Three strategies were tested: (1) with all available variables, (2) with a filter-based variable selection, and (3) with a wrapper-based variable selection which integrates Boruta algorithm and random forest. Prediction models of energy cost are created using two approaches: (a) comparative usage of artificial neural networks and two types of regression trees, CART and random forest, and (b) integration of RF-Boruta variable selection and machine learning methods for prediction. A cross-validation procedure was used to optimize the artificial neural network and regression tree topology, as well to select the most appropriate activation function. Along with creating a prediction model, the aim of the paper was also to extract the relevant predictors of energy cost in public buildings which are important in planning the construction or renovation of buildings. The results have shown that the second approach which integrates machine learning with Boruta method, where the random forest algorithm is used for both variable reduction and prediction modeling, has produced a higher accuracy of prediction than the individual usage of three machine learning methods. Such findings confirm the potential of hybrid machine learning methods which are suggested in previous research, but in favor of random forest method over CART and artificial neural networks. Regarding the variable selection, the model has extracted heating and occupational data as the most important, followed by constructional, cooling, electricity, and lighting attributes. The model could be implemented in public buildings information systems and their IoT networks within the concept of smart buildings and smart cities.