When I graduated 2 years ago, starting salary for a new grad at St Thomas (including what was then Baptist and MTMC) was $18.50, not including shift differentials. Centennial, and probably the other local HCA hospitals, was $19.96, again without including shift diffs. These may have increased since then. Not sure about Vanderbilt or other hospitals (Williamson Medical Center, Gateway, Sumner Regional, etc), though the VA likely has the highest starting salary for new grads. I am currently working at an outpatient GI clinic and endoscopy lab making $25 per hour + OT.
Be forewarned that while the health care industry in Middle Tennessee is robust, there are a LOT of nursing schools
here cranking out loads of new nurses twice per year and competition for hospital positions for new grads can be fierce. Good luck!