What is the name of the city and neighborhood in Israel where the ultra-orthodox live?

Answer 1

THE city? THE neighbourhood? You talk as if you expect there to be only one!
Aproximately 25% of Israel's population is Orthodox. A sizable percentage of that is "ultra Orthodox". Translation: Expect the demographics to indicate that they live in more than one place.
For the record, some well known religious neighbourhoods/cities in Israel...
Bnei Brak (city near Tel Aviv)
Mea Shearim - (neighbourhood in Jerusalem)