The vicinity of the supermassive black hole associated with the compact radio source Sagittarius ( Sgr ) A* is believed to dominate the observed emission at wavelengths near and shorter than \sim 1 millimeter . We show that a general relativistic accretion flow , heated via the plasma wave heating mechanism , is consistent with the polarization and recent mm-VLBI observations of Sgr A* for an inclination angle of \sim 45 ^ { \circ } , position angle of \sim 140 ^ { \circ } , and spin \lesssim 0.9 . Structure in visibilities produced by the black hole shadow can potentially be observed by 1.3 mm-VLBI on the existing Hawaii-CARMA and Hawaii-SMT baselines . We also consider eight additional potential mm-VLBI stations , including sites in Chile and New Zealand , finding that with these the basic geometry of the emission region can be reliably estimated .