But the couple didn't meet her parents as reported – that Internet photo shows her brother at Father's Day, PEOPLE has learned

Taylor Swift‘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.

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“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.

Writes another: “All I know is that she seems so, so happy right now and when Taylor is happy, so am I!”

Another photo posted by a fan shows Swift dining with her parents and a young man with shaggy hair.