The dynamics of water confined to nanometer-sized domains is important in a variety of applications ranging from proton exchange membranes to crowding effects in biophysics. In this work, we study the dynamics of water in gemini surfactant-based lyotropic liquid crystals (LLCs) using molecular dynamics simulations. These systems have well characterized morphologies, for example, hexagonal, gyroid, and lamellar, and the surfaces of the confining regions can be controlled by modifying the headgroup of the surfactants. This allows one to study the effect of topology, functionalization, and interfacial curvature on the dynamics of confined water. Through analysis of the translational diffusion and rotational relaxation, we conclude that the hydration level and resulting confinement length scale is the predominate determiner of the rates of water dynamics, and other effects, namely, surface functionality and curvature, are largely secondary. This novel analysis of the provides an important comparison for previous studies of water dynamics in lipid bilayers water dynamics in these LLC systems and reverse micelles.