The Gemara discusses cities that are close to Yerushalayim (or close to walled cities from Yehoshua's time). Cities that can "see" the walled cities (close suburbs) would also read the Megilla on the 15th of Adar.
(a) Do those suburbs have to have existed at the time of Yehoushua also? How does this affect most of the new city of Yerushalayim outside the old city walls? What about all of the modern neighborhoods such as Gilo and Bakka? What about newer neighborhoods such as Har Nof or Ramot? What about newer towns such as Mevasseret or Maale Adumim that can see Yerushalayim? Do they read on the 14th or 15th of Adar or both?
(b) Are there any other towns that definitely had a wall at Yehoshua's time? Also, do we know where Shushan Habira is today and does it read the megilla on the 15th of Adar?
(a) The nearby city does not have to have been there from the times of Yehoshua. Rather, it is subordinate to the walled city to which it is near, and that walled city must have been walled from the times of Yehoshua. That applies also to the new parts of Yerushalayim. (The Rambam, though, holds that the nearby city must be within one Mil of the walled city, and it is not sufficient to be just within sight of the walled city. The Rishonim do not accept the Rambam's ruling, and thus a city that is within sight of a walled city, even though it is very far away, is considered part of the walled city with regard to reading the Megilah. Some Rishonim require that there be Asarah Batlanim in the walled city.)
However, this applies only when the nearby city can see the walled city itself, and not when the nearby city can only see another city which is near the walled city. It suffices to see the wall of the city from part of the nearby city, even if the wall cannot be seen from the place where the Megilah is being read.
In modern Yerushalayim, places like Har Nof, Ramot, and Mevaseret do not see the wall of the Old City at all, and for that reason many Poskim have ruled that those places should read the Megilah on the 14th of Adar. However, others rule that whenever the area between the far-away neighborhood (such as Har Nof) and the place from which the wall can be seen is continuously full of residential dwellings, it is all considered one city. For this reason, the common practice today is to read the Megilah on the 15th of Adar in Har Nof. Regarding Ramot, the Poskim disagree whether this principle applies, because there is an unsettled valley separating between Ramot and the rest of Yerushalayim. Most residents of Ramot read the Megilah on the 15th, reasoning that since the Eruv of Yerushalayim includes Ramot, it is all considered one city, and thus they read on the 15th just like the other neighborhoods which are close to the walled city.
This reasoning does not apply to the neighborhoods which are even farther from the city, such as Ma'aleh Adumim and Mevaseret, although there are some in those communities who do read on the 15th, but their reasoning is not clear.
(b) 1. Teverya (Tiberias) was definitely walled from the times of Yehoshua. It has a Safek when to read the Megilah for a different reason, as explained in the Gemara (5b).
2. Yafo (Jaffa) was walled from the times of Yehoshua.
3. I have heard that in Lublin, they used to read the Megilah on the 15th, since it was close to a city that was walled "from time immemorial." (See, however, RITVA here, regarding cities in Europe.)
4. Today's Yericho is not in the same location as the Yericho that was walled at the times of Yehoshua.
5. There are many who maintain that Shushan is the modern city of Hamadan, in Iran. The graves of Mordechai and Esther are located there. Regarding when to read the Megilah there, ask your local rabbinical authority.
All the best,