Northern Kazakhstan is considered a field of uranium, gold mining, copper–molybdenum ore, and other metals. The aims of the current work were to monitor the indoor radon levels in a school and a kindergarten and to determine the levels of teacher and student exposure to radon. High radon concentrations were detected in the school on the first floor at ca. 9600 Bq/m³, on the second floor at ca. 6800 Bq/m³, on the third floor at ca. 4900 Bq/m³, and in the kindergarten, the concentration was ca. 9500 Bq/m³. The annual effective dose of the students and teachers of the school and kindergarten varied from 4 mSv/y to 9 mSv/y, which is an order of magnitude higher than the upper annual dose limit. The excess lifetime cancer risk was 14–20% for students, 31.1% for school and kindergarten staff, and 34.9% for kindergarten children. The indoor radon concentrations varied with weather conditions, and it was evident that ventilation had a significant effect on the reduction in the concentration. At these premises, positive correlations between the radon concentrations, outside temperature, and relative humidity were obtained, showing that the concentration of radon is influenced by meteorological parameters. This study will help to identify buildings where continuous monitoring is needed in order to reduce indoor radon levels.