There is a free bus that goes on fifth and one that goes on fourth. Green bus or blue bus.
As Meg said, surface lots are oddly expensive and to be avoided but there are several near The Ryman, to include a half-block away at 5th and Commerce. For events, The Ryman has valet, if you're looking for ease of use. Otherwise, I'd recommend the building at 210 Commerce, the meters between the federal building and the Frist on 9th South, downriver from Nissan Stadium by Cumberland Park (and cross the pedestrian bridge), or the Frist parking itself.
Two. Blocks down from it-across broadway are many meters. And lots. lots are crazy expensive. Past bridge-downtown there are streets with meters. couple of blocks walk. OR across from Visitor's Center is a building has pay garage in it.
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