Hier war das Ufer unserer Begegnung
Unserer Begegnung is a genitive supplement to das Ufer. It's the standard way to describe features of things.
Hier war das Ufer von unserer Begegnung
is considered really bad German. It's understood but you show bad command of the language if you talk like this. It may be used for effect.
Please don't confuse it with prepositional objects led by von. Some verbs have these. In the following example, you have both the prepositional object and a genitive supplement to that object:
Sie erzählt von der Reise der Tochter.
She tells about the journey of the daughter.
See how der Tochter has no preposition in front of it. In better English, you would write
She tells about the daughter's journey.
So daughter's is genitive in English, too. German extends this to things.
Hier war das Ufer unserer Begegnung.
Here was our encounter's shore.
May be valid as poetical English?