I'd like to get some new ideas for elegant/interesting places to go for tea or a drink or snack, alone or with a friend. The quality of the food/drink is not of prime importance for the purpose of this request - I'm interested in the setting - establishments that have nice/unique interior design or architecture, or that may be of historical interest. Vintage or antique furnishings a plus. (I'm trying to avoid using that empty word "atmosphere" here...) Places that have character, that (in your opinion) are special, or simply cozy. To be clear, I don't care about how hip the place is, I prefer low-key anyway. No blaring top 40 music, to be sure.
I realize my question is pretty vague and hinged on subjectivity but basically I would like to visit some new-to-me places in the city and would love to read your suggestions! Anything from your neighbourhood haunt to a museum cafe or hotel bar... as long as it has *ahem* atmosphere.