  Current experiments at the Relativistic Heavy Ion Collider (RHIC) are probing
finite baryon densities where the shear viscosity to enthalpy ratio $\eta T/w$
of the Quark Gluon Plasma remains unknown. We use the Hadron Resonance Gas
(HRG) model with the most up-to-date hadron list to calculate $\eta T/w$ at low
temperatures and at finite baryon densities $\rho_B$. We then match $\eta T/w$
to a QCD-based shear viscosity calculation within the deconfined phase to
create a table across $\left\{T,\mu_B\right\}$ for different cross-over and
critical point scenarios at a specified location. We find that these new $\eta
T/w(T,\mu_B)$ values would require initial conditions at significantly larger
$\rho_B$, compared to ideal hydrodynamic trajectories, in order to reach the
same freeze-out point.
