Translation:Tiberias is found on the shores of the Sea of Galilee.
By far the simplest way to say this in English is the same way it's said in Hebrew:
Tiberias is on the Sea of Galilee.
In this context, "on" doesn't literally mean on top of, but rather next to. Paris is on the River Seine, New York is on the Atlantic Ocean, Israel is on the Mediterranean, and Tiberias is on the Kinneret.
How about "Tiberias is found on the mouth of the Kinneret/Sea of Galilee"?
It is fine in English, I am just not sure whether it is a correct Hebrew translation.
When talking about bodies of water, the mouth is specifically where a river meets a larger body. Mouth as a synonym for rim is more used for things like bottles.
We'd use mouth to talk about rivers, the area where the river meets a larger body of water, but I've never heard it used the way you're suggesting. Do you have a dictionary entry to back that up?