  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.
