I don't have a good map with dates for each city, but I do have dates on some notable cities from my notes! I'm in a class on the Ancient Mediterranean.

In general we can tell if a city was attacked or not through archaeological evidence. Cities like Troy (VIIa)*, Gibala, and Ugarit were considered razed because a lot of arrowheads were found embedded in walls & buildings, skeletons show signs of non-crushing violent injury and there is evidence of widespread fires.

In contrast cities like Troy (VI)* and Tiryns were likely destroyed by earthquakes because skeletons show signs almost exclusively of crushing injuries, buildings are destroyed but without any evidence for weapons or (significant) fire, and the specific destruction pattern for the buildings. ((Invaders don't shake blocks out of all of the buildings in a city))

*Troy VI and Troy VIIa are both in the same location, but they're different archaeological layers. i.e. Troy VI was destroyed by an earthquake, but the people rebuilt after the destruction.

This is one of my favorite periods in history and I too question what was going on in the surrounding areas beyond the Mediterranean, especially up in Europe. We know that there was trade coming from Europe such as tin and amber, and the amber was coming from pretty far north so at least some people up in Europe knew about these Mediterranean cultures!