We present the results from our survey of HI 21-cm absorption, using Giant Metrewave Radio Telescope, Very Large Array and Westerbork Radio Synthesis Telescope, in a sample of 55 z<0.4 galaxies towards radio sources with impact parameters (b) in the range ~0-35kpc. In our primary sample (defined for statistical analyses) of 40 quasar-galaxy pairs, probed by 45 sightlines, we have found seven HI 21-cm absorption detections, two of which are reported here for the first time. Combining our primary sample with measurements having similar optical depth sensitivity ({int}{tau}dv<=0.3km/s) from the literature, we find a weak anti-correlation (rank correlation coefficient =-0.20 at 2.42{sigma} level) between {int}{tau}dv and b, consistent with previous literature results. The covering factor of HI 21-cm absorbers (C21) is estimated to be 0.24^+0.12^_-0.08_ at b<=15kpc and 0.06^+0.09^_-0.04_ at b=15-35kpc. {int}{tau}dv and C_21_ show similar declining trend with radial distance along the galaxy's major axis and distances scaled with the effective HI radius. There is also tentative indication that most of the HI 21-cm absorbers could be co-planar with the extended HI discs. No significant dependence of {int}{tau}dv and C_21_ on galaxy luminosity, stellar mass, colour and star formation rate is found, though the HI 21-cm absorbing gas cross-section may be larger for the luminous galaxies. The higher detection rate (by a factor of ~4) of HI 21-cm absorption in z<1 damped Lyman-{alpha} systems compared to the quasar-galaxy pairs indicates towards small covering factor and patchy distribution of cold gas clouds around low-z galaxies.