In the South East, they bring you sweetened (usually far too sweetened for my tastes) iced tea. This is amazingly universal.
I live in NC and have been probing the border for years.
For “nicer” restaurants, the universal sweet tea boundary seems to be precisely at the NC/VA border.
We don’t drink tea in the same way as the British, but sweet tea is an extremely common drink in the south-east us. It’s almost certainly the top drink after soda and water.