The translational self-diffusion coefficients (D-T) for a series of tetra-alkyl acyclic ammonium and cyclic pyrrolidinium ionic liquids (ILs) were measured using H-1 pulse field gradient (PFG) NMR spectroscopy over various temperatures. These NMR diffusion results were combined with previously measured rotational diffusion coefficients (D-R) obtained from N-14 NMR relaxation measurements for the same ILs (Alam, T. M.; et al. J. Phys. Chem. A 2011, 115, 4307-4316). The D-T/D-R ratio was then used to estimate the effective hydrodynamic radius and corresponding volumes without the need to directly measure the viscosities of the ILs. The generality, validity, and performance of using this D-T/D-R ratio is discussed and compared to the effective hydrodynamic volumes obtained using classic D-T/viscosity and D-R/viscosity relationships. The temperature variation observed for the molecular volumes obtained using the D-T/D-R ratio is argued to be a signature for the breakdown or decoupling of the Stokes-Einstein and Stoke-Einstein-Debye relationships in these neat IL systems, consistent with recent molecular dynamic simulations.