Will The Real Yerushalayim PLEASE Stand Up

The gemara in Bava Kamma [פב] talks about 10 special laws that apply only in Yerushalayim. What is Yerushalayim? Only within the ancient walls of Yerushalayim is considered Yerushalayim. The wall we have today is only about 400 years old. It is not clear how far the ancient walls extended and there are various opinions. But for example Har Nof and Bayit Vegan and most likely even Rechavia/Talbieh were outside the ancient walls. So those laws mentioned in the gemara wouldn't apply to those places.

Today as well there are various customs that apply only in "Yerushalayim". The halacha is that if there is no aron kodesh in the room we don't fall on out face for תחנון. But everywhere in Yerushalayim is considered before the ארון השם [!] so here we fall on our face even when there is no aron kodesh in the room. The customs that the residents of Yerushalayim accepted upon themselves apply even in the "new city", those neighborhoods that were appended to Yerushalayim. So apparently, even in the Inbal or the King David hotels one would fall on one's face for תחנון even in the absence of a sefer torah. The same would apply to the custom of lighting shabbos candles 40 minutes before sunset and the custom of not treating the fruits of goyim as having kedushas shviis.

עיין שו"ת משנת יוסף ח"ה סי' ל"א