When I can't find something to watch I go right to Turner classic. I love those old movies. The way they dressed, spoke, carried themselves, and the way the homes eyes decorated. Most of the movies are American, but they talk with an accent I can't put my finger on.
What you're hearing is "The Mid-Atlantic Accent" that was taught in US boarding schools and to stage actors in the early part of the 20th century:
https://en.m.wikipedia.org/wiki/Mid-Atlantic_accent