Solid polymer electrolytes are ionically conducting phases formed by dissolving salts in an amorphous polymer matrix. In this study, the local structure and dynamics of Na+ and I- ions in molecular dynamics (MD) simulations of the amorphous poly(ethylene oxide)-based electrolyte PEO(x)NaI (x=48,20,3) are analyzed at both 400 and 500 K. The fully atomistic model reproduces many phenomena seen experimentally and provides a picture of the complex correlations between cation, anion, and polymer host in these systems. The composition of the first coordination shell around the cations illustrates the concentration-dependent competition between iodines and PEO backbone oxygen atoms to coordinate the positively charged cations. Contiguous polymer segments tend to form near-planar polydentate loops around the sodiums while the anions are usually placed above and/or below the PEO ... Na+ quasiplane. This geometry results in optimal coordination of both types of ligands to the cation in a similar pattern to that found in crystalline PEG-based systems and crown ethers. Although the observation of large-scale diffusion is still effectively precluded by the currently accessible MD time scale, discrete ligand exchanges do occur in the coordination shell of the cations. Examples of these dynamical events, including various jumps between local potential coordination sites, are shown and their net result on ionic motion is discussed.