The River Brandywine formed the eastern boundary of The
Shire, in
Middle-earth. It rose in
Lake Evendim or
Nenuial and flowed south. The
Old Forest was on the eastern side of it, just outside the Shire. The
Buckland, the area where the
Brandybuck family lived, was part of the Shire on the far side of the river.
Tolkien no doubt got the name from the famous Brandywine battle in America, but he made out it was an alteration of the Elvish name Baranduin, which means "golden-brown river".
Brandy the drink is short for "brandywine", which comes from the Dutch for "burnt wine".