Taylor Swift and Conor Kennedy
Cindy Ord/Getty; Douglas Healey/Polaris
08/10/2012 at 06:50 PM EDT
's love story with Conor Kennedy
is moving to her home turf.
On Thursday, Swift, 22, and Kennedy, 18, were spotted at Edley’s BBQ
in Nasvhille, where she posed for pictures with fans.
"They were both very relaxed and casual and for the most part were left alone to enjoy their dinner with a friend," one fan writes of the couple
: "All I know is that she seems so, so happy right now and when Taylor is happy, so am I!"
posted by a fan shows Swift dining with her parents and a young man with shaggy hair.
Despite widespread reports that this was Conor meeting her parents, the photo actually depicts her brother at a Father's Day meal in June, Swift's rep tells PEOPLE.