We investigate the transport properties of a model of a hydrated Na-Nafion membrane using molecular dynamics simulations. The system consists of several Nafion chains forming a pore with the water and ions inside. At low water content, the hydrophilic domain is not continuous and diffusion is very slow. The diffusion coefficient of both water and Na+ increases with increasing hydration (more strongly so for Na+). The simulations are in qualitative agreement with experimental results for similar systems. The diffusion coefficient is an average over the motion of ions or water molecules located in different environments. To better understand the role of the environment, we calculate the distribution of the residence times of the ion (or water) at different locations in the system. We discuss the transport mechanism in light of this information.