The Hobbit Frodo Baggins regularly visited the inn as did his friends Sam Gamgee, Meriadoc Brandybuck and Peregrin Took. Throughout the movie and the book, the inn is referenced to as a "great" place. One such example in when Merry and Pippin refer to the Inn in The Return of the King (film) when they are singing on a table at Edoras. Specifically, they sing "The Green Dragon (song)"
In the video game The Fellowship of the Ring you can enter the Green Dragon Inn and talk with the Head Sheriff about the wolves that have been entering the Shire and speak with other hobbits to get an idea of the general lifestyle of a hobbit. Also, this is the place where Bilbo Baggins meets up with Gandalf and the Dwarves.