Are you going to be camping in the immediate area? Some of the campgrounds out on Music Valley Drive may have transportation arrangements available to downtown.
The Nashville Tourism Bureau @ (615) 259-4700 may can tell you if parking is available close by. Downtown parking is expensive, however.
Another option would be to park at a shopping center and catch public transit to downtown. Downtown is scarcely any longer than a 15 minute ride from anywhere intown. See: Nashville MTA Maps and Schedules - bus maps, bus schedules
Nashville's a great city to visit, and it is truly Music City USA.