Hello, Seby, and welcome.

Outside of a genuine tea-house it is still true that the best tea in a
restaurant is the tea you bring yourself.

I live in New York City, and here many places, even delis, have a variety of
bagged tea (black, green, flavored). At least it is not all just black tea
anymore. However, it is still no better than poor-to-average.

I have had good success being served hot water when I bring my own tea. The
trick is remembering to bring along the tea when I go out.

Joe