This is all I can find (starting from the south and heading north...):-
The land of Philistia (on the coast, parallel with the Dead Sea):-
Gaza, Ascalon, Ashdad, Ekron, Joppa, Eltekeh,
The land of Canaan, later Judah (between Philistia and the Dead Sea):-
Beer-Sheba, Lachish, Arad, Gath, Hebron, Jerusalem, Gilgal, Bethel,
The land of Edom (south of Canaan), --no known cities--
(although Solomon built a fortress way down south on the Red Sea coast called Ezion-geber)
The land of Moab (east of the Dead Sea), --no known cities--
(although Solomon built a fortess on the southern tip of the Dead Sea called Tamar)
The land of Samaria, later Israel (north of Canaan, but not on the coast):-
Silo, Shecham, Ganzim, Samaria, Tirzah, Gezer, Tabor, Nazareth, Megiddo, Beth-shean, Hazor
The land of Ammon (north of Moab):-
Rabbah,
In Phoenicia (on the coast, north of the Sea of Galilee):-
Acco, Tyre, Sidon, Byblos,
In the land of Aram (inland, parallel with Phoenicia):-
Dan, Damascus, Riblah,
In the Levant (on the coast north of Phoenicia):-
Arvad, Ugarit, and inland is Qadesh, Hamath, Qarqar, Aleppo, Carchemish,
The only Egyptian city I can find west of Edom is Raphia, and I can find no cities east of Ammon/Moab, probably because of the desert.
And thats all I'm afraid. Hope it's of some use and good luck.