A systematic study of the indoor airborne radon concentration in the central part of the Nicosia district was conducted, using high-sensitivity active radon portable detectors of the type "RADIM3A". From a total of 108 measurements in 54 grids of 1 km^2 area each, the overall mean value is 20.6 \pm 13.2 Bq m^-3 (A.M.\pm S.D.). That is almost twice less than the corresponding average worldwide value. The radon concentration levels in drinking water were also measured in 24 sites of the residential district, using the high-sensitivity radon detector of the type "RADIM3W". The mean value obtained from these measurements is 243.8 \pm 224.8 mBq L^-1, which is relatively low compared to the corresponding internationally accepted level. The associated annual effective dose rates to each measurement were also calculated and compared to the corresponding worldwide values. From the geographical coordinates of the measuring sites and the corresponding radon concentration values, the digital radon map of the central part of the Nicosia district was constructed for the first time, by means of the ArcMap software package.