I doubt that. The factions are far apart from each other and some are grave enemies of each other and would pretty much never trust the other to not backstab them.
To be honest, the only faction that isn't allowed in any neutral territory is Noxus. That's because of their expansionist world view (think of America's manifest destiny). They will keep going and going. The moment they set foot somewhere, even if preoccupied, they want to keep it for themselves.
With that being said, Piltover and Bilgewater seem like proper port towns for other cities kingdoms and hte like would gather. It's just that it would be business as per usual in the markets. Noxians might be okay in BW purely because of the environment, but PIltover has a wary eye since they're next door to Shurima that is going through an incursion of Noxians at the moment.
If what you're asking for is UN levels of neutrality and peace talks...they're non-existent.
Piltover is a city of trade and invention and does not seem to have much offensive military, so it's likely the most peaceful/neutral place in Runeterra when someone from Zaun isn't ravaging it. Same can be said about Bilgewater, but it's a little more shady.