Solutions of glucose, cellobiose, and microcrystalline cellulose in the ionic liquid 1-ethyl-3-methyl-imidazolium acetate ([C2mim] [OAc]) have been examined using low-field (20 MHz) NMR relaxometry and rheology. The spin-lattice (T-1) and spin-spin (T-2) relaxation times have been determined from 30 to 70 degrees C inclusive, for a range of concentrations (0-15 wt %) of each carbohydrate in [C2mim][OAc]. The zero shear rate viscosities for the same samples across the same temperature range were studied. The viscosity, NMR relaxometry, and previously published diffusion data were all analyzed together through the Debye-Stokes-Einstein equations. Microscopically, these systems behave as an "ideal mixture" of free ions and ions associated with the carbohydrate molecules. The molar ratio of carbohydrate OH groups to ionic liquid molecules, alpha, is the key parameter in determining the NMR relaxometry and hence the local microscopic environment of the ions. NMR relaxometry data are found to follow an Arrhenius type behavior, and the difference in rotational activation energy between free and associated ions is determined at 6.2 +/- 0.5 kJ/mol.