The Blue Parrot Café is an establishment on Sarona VIII. The Blue Parrot was build in the shape of the Saronan emblem - a dodecahedron that was vaguely crescent shaped. The cafe catered mainly to visitors to the nearby conference center. (TNG novel: A Time for War, A Time for Peace)
Among its attractions were blue cocktails which the crew of the USS Enterprise-D were looking forward to trying when they stopped there for shore leave in 2364. (TNG episode: "We'll Always Have Paris")
In 2379 Esperanza Piñiero met Jas Abrik in the Blue Parrot Café to ask him to not reveal what he knows about Tezwa and to offer him the job of security advisor to Nanietta Bacco, should she win the election for Federation President.