All American restaurants serve tea.
The big snag is in the South, where iced tea is called sweet tea and is only served with sugar in it. Yuck! And come to think of it, I've been in Indian restaurants herethat only serve hot tea sweetened. Lucky their food is so good!
Some trendy neighborhoods have so-callled tea shops and tea rooms that serve tea, but oddly enough, it's not usually very good.
We have lots of coffee shops, but the meaning of the term is different from place to place. In New York City, it's a diner. In most places, it's a place that specializes in coffee. That's where you go for a mocha latte grande, for instance.
(By the way, when I say diner, I'm using this Merriam Webster definition of an American diner: "a typically small, informal, and inexpensive restaurant that has an extensive menu . . . .")
Likewise, the word cafe has different meanings in different parts of the country. In the east, it's a bistro or a casually fancy restaurant. In the west, it's a diner.
And as I recall, the Pacific Northwest is full of espresso bars. You can imagine what goes on there.
And that's as much as I can think of on the subject, as I sit here sipping a hot cup of organic Assam — unsweetened, of course!