I visited a pal in Nashville last fall, and we made a quick trip out to South Cumberland State Park, a little over an hour east. I looked at cabins in the area (though ended up opting for a hotel in Jasper because we only stayed a night) and there seemed to be lots of them available, and the excellent Fiery Gizzard trail might meet your overnight needs. Beautiful country!
@Rob_U Thanks for the advice. The Fiery Gizzard looks awesome. I love finding gems in the Midwest!