The recent fabrication of liquid crystalline ion gels featuring rigid-rod polyanions aligned within room-temperature ionic liquids (RTILs) opens up exciting new avenues for engineering ion conducting materials. These gels exhibit an unusual combination of properties including high ionic conductivity, distinct transport anisotropy, and widely tunable elastic modulus. Using molecular simulations, we study the structure and dynamics of the ions in an ion gel consisting of rigid-rod polyanions and [C(2)mim] [TfO] RTILs. We show that the ion distribution in the interstitial space between polymer rods exhibits the hallmarks of the RTIL structure near charged surfaces; i.e., cations (C(2)mim(+)) and anions (TfO-) form alternating layers around the polymer rods and the charge on the rod is overscreened by the ionic layer surrounding it. The distinct ordering of ions suggests the formation of a long-range "electrostatic network" in the ion gel, which may contribute to its mechanical cohesion and high modulus. The dynamics of both C(2)mim(+) and TfO- ions slow down due to the fact that some C(2)mim(+) ions become associated with the sulfonate groups of the polymer rod on nanosecond time scales, which hinders the dynamics of all ions in the gel. C(2)mim(+) and TfO- ion diffusion in the gel are only 2-10 times slower than in bulk RTILs, which is still much faster than, e.g., Li ions in typical ion conducting polymers. This fast ion transport combined with strong mechanical cohesion open up exciting opportunities for application of these gels in electrochemical devices including Li-metal batteries.