Enhanced dynamical fluctuations of RNAs, facilitated by a network of water molecules with strong interactions with RNA, are suspected to be critical in their ability to respond to a variety of cellular signals. Using atomically detailed molecular dynamics simulations at various temperatures of purine (adenine) and preQ(1) sensing riboswitch aptamers, which control gene expression by sensing and binding to metabolites, we show that water molecules in the vicinity of RNAs undergo complex dynamics depending on the local structures of the RNAs. The overall lifetimes of hydrogen bonds (HBs) of surface-bound waters are more than at least 1-2 orders of magnitude longer than those of bulk water. Slow hydration dynamics, revealed in the non-Arrhenius behavior of the relaxation time, arises from high activation barriers to break water HBs with a nucleotide and by reduced diffusion of water. The relaxation kinetics at specific locations in the two RNAs show a broad spectrum of time scales reminiscent of glass-like behavior, suggesting that the hydration dynamics is highly heterogeneous. Both RNAs undergo dynamic transition at T = T-D greater than or similar to 200 K, as assessed by the mean-square fluctuation of hydrogen atoms < x(2)>, which undergoes an abrupt harmonic-to-anharmonic transition at T-D. The near-universal value of T-D found for these RNAs and previously for tRNA is strongly correlated with changes in hydration dynamics as T is altered. Hierarchical dynamics of waters associated with the RNA surface, revealed in the motions of distinct classes of water with well-separated time scales, reflects the heterogeneous local environment on the molecular surface of RNA. At low temperatures, slow water dynamics predominates over structural transitions. Our study demonstrates that the complex interplay of dynamics between water and the local environment in the RNA structures could be a key determinant of the functional activities of RNA.