Stay at the Milon Ron. It’s the nicest place that you can get Mehadrin meals and is not a far walk from the Old City.
Friday night keep away from the Carlebach minyan, it’s ridiculously packed and you may end up standing outside on the street.
The real Breslov shul next to the Bais HaChaim is very nice and there is a lot of nice Chassidish singing during davening with a minimum of meshuggenas.
The Ari z”l shuls are also beautiful.