Indoor radon and meteorological parameters (temperature, humidity, pressure, precipitation, indoor dew point, wind direction, wind speed and heat index) were simultaneously monitored in an old residential house in a radon suspected area. Measurements were performed during the period from winter to summer (13 February 2021–15 August 2021). Indoor radon concentrations were measured with detectors, Airthings Corentium Home (alpha spectrometry method), and meteorological parameters were continuously monitored by the meteorological station WTH600–E (wireless weather station). The influence of geological characteristics in the study area was analyzed, as well as some observed variations and correlations with indoor/outdoor meteorological parameters. The results indicated that indoor radon levels are higher in the spring/summer season than in the winter season. Diurnal radon concentrations varied during measuring period from 303–1708 Bq/m3 (average 949 Bq/m3) and 427–1852 Bq/m3 (average 1116 Bq/m3) for the living room and bedroom, respectively. Indoor radon concentrations correlated with: outdoor/indoor temperature, indoor humidity (r = 0.45, r = 0.40, r = 0.32, r = 0.56, respectively); indoor dew point (r = 0.53); outdoor barometric pressure (r = −0.26); there were no clear correlation with precipitation and outdoor humidity. The health risk due to long-term, high radon exposure was assessed through the calculated inhalation dose.