I lived in Givat Shaul (right above the entrance to the city) for 5 years, but that area is anything but anglo. Just 100% Israeli chareidi (note many residents wouldn’t like being called Israeli though!), mostly Hebrew/Yiddish-speaking.
That said, there are some Americans, Britons, South Africans, and in the new area (Kehati) a lot of French.
It’s very mixed, everything from Edah (Satmar etc) to Mizrachim, some dati leumim, Litvishe, everything in between you could possibly imagine.
I absolutely loved it there and it was very difficult for me to leave there and move to Gateshead.
As for other neighborhoods: Har Nof has a lot of Americans, as does Bait VeGan. They are further away from the city though, whereas Givat Shaul is exactly 30 mins walking from Kikar Shabbat and less than 1 hour from the Kotel.