Earlier in the week, the new couple spent time in Nashville, where they danced and cuddled at Selena Gomez's concert – getting particularly close during Gomez's hit "Hands to Myself." On Wednesday evening, the pair had a dinner date at Ruth's Chris Steakhouse.
After meeting Swift's parents on Thursday, the couple dined at farm-to-fork restaurant Adele's in downtown Nashville, with singer-songwriter Holly Williams and her husband Chris Coleman. Hiddleston played Holly's grandfather Hank Williams in the film I Saw the Light.
Swift and Hiddleston went public with their romance earlier this month. The duo were photographed kissing a few weeks ago, holding hands and cuddling on the beach in Rhode Island.
PEOPLE exclusively broke the news earlier this month that Swift and her ex, Calvin Harris, had split after 15 months of dating.