Current experiments at the Relativistic Heavy Ion Collider (RHIC) are probing finite baryon densities where the shear viscosity to enthalpy ratio ηT /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 ηT /w at low temperatures and at finite baryon densities ρB. We then match ηT /w to a QCD-based shear viscosity calculation within the deconfined phase to create a table across {T, µB} for different cross-over and critical point scenarios at a specified location. We find that these new ηT /w(T, µB) values would require initial conditions at significantly larger ρB, compared to ideal hydrodynamic trajectories, in order to reach the same freeze-out point.1 Note that at finite µ B the enthalpy w = ε + p is used rather than entropy 2 Alternatives to η/s(T, µ B = 0) = 0.08 exist [14-17] at vanishing baryon densities where an action is formulated that allows for derivatives up to the 4th order. However, these calculations have not yet been incorporated into non-conformal AdS. Since nonconformality is vital for understanding the QCD phase transition, the current framework cannot provide non-trivial information about η/s(T, µ B ) at a critical point.