Water dynamics in the solvation shell around biomolecules plays a vital role in their stability, function, and recognition processes. Although extensively studied through various experimental and computational methods, dynamical time scales of water near DNA is highly debated. The residence time of water is one such dynamical quantity that has been probed rarely around DNA using computational methods. Moreover, the effect of local DNA sequence variation in water residence time has also not been addressed. Using 20 DNA systems with different sequences, we capture here the mean residence time (MRT) of water molecules around 360 different sites in the major and minor grooves of DNA. Thus, we show that a distribution of time scales exists even for a regular structure of DNA, reflecting the effect of chemistry, topography, and other factors governing dynamics of water. We used the stable state picture (SSP) formalism to calculate MRT that avoids the effect of transient recrossing. Results obtained from simulations agree well with experiments done on a few specific systems at a similar temperature. Most importantly, we find that although the groove width and depth influence water time scale, MRT of water is always longer in the middle of the DNA, in agreement with NMR experiments. We propose a simple kinetic model of water escape from DNA where water molecules move along the DNA and perpendicular to it in both the first and second solvation shell before it escapes to bulk. We show that this simple kinetic model captures both the time scale and the position dependence of MRT of water around DNA. This study thus portrays the origin and a measure of heterogeneity in water dynamics around DNA and provides a fresh perspective in the ongoing debate on water dynamical time scales around DNA.