The recent detection of Sagittarius A* at lambda = 1.3 mm on a baseline from Hawaii to Arizona demonstrates that millimeter wavelength very long baseline interferometry (VLBI) can now spatially resolve emission from the innermost accretion flow of the Galactic center region. Here, we investigate the ability of future millimeter VLBI arrays to constrain the spin and inclination of the putative black hole and the orientation of the accretion disk major axis within the context of radiatively inefficient accretion flow (RIAF) models. We examine the range of baseline visibility and closure amplitudes predicted by RIAF models to identify critical telescopes for determining the spin, inclination, and disk orientation of the Sgr A* black hole and accretion disk system. We find that baseline lengths near 3 gigalambda have the greatest power to distinguish amongst RIAF model parameters, and that it will be important to include new telescopes that will form north-south baselines with a range of lengths. If a RIAF model describes the emission from Sgr A*, it is likely that the orientation of the accretion disk can be determined with the addition of a Chilean telescope to the array. Some likely disk orientations predict detectable fluxes on baselines between the continental United States and even a single 10-12 m dish in Chile. The extra information provided from closure amplitudes by a four-antenna array enhances the ability of VLBI to discriminate amongst model parameters.
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