The best site for government sources will be the Tennessee State Library Archives. Collections such as this one from the Department of Conservation may be useful, though they would have to be accessed at the archive building. Here is a link to a guide on legal and legislative materials at TSLA.
Searching for Nashville city legislation records: Legistar and Legisarchive.
Nashville.gov's page about park names
Nashville Planning department's parcel viewer:
Sanborn Fire Insurance maps: Limit to Davidson County
Nashville Public Library's maps
What Nashville Public Library can do. Note that their holdings may include architectural drawings or maps of parks.