Neo4j's pricing is actually quite flexible, so don't be put away by the prices on the website.
You can also get started with the community edition or personal edition for a long time.
The Neo4j community is very active and helpful and quickly provide support and help for your questions. I think that's the biggest plus besides performance and convenience. I
n general using a graph model
Regarding your use-case:
Neo4j is used exactly for this route calculation scenario by one of the largest logistic companies in the world where it routes up to 4000 packages per second across the country.
And it is used in other game engines, like here at GameSys for game economy simulation and in another one for the routing (not in earth coordinates but in game-world-coordinates using Neo4j-Spatial).
I'm curious why you have only that few nodes? Are those like transport portals? I wonder where you store the details and the dynamics about the routes (like the criteria you mentioned) are they coming from the outside - in memory state of the game engine?
You should probably share some more details about your model and the concrete use-case.
And it might help to know that both Emil, one of the founders of Neo4j and I are old time players of multi user dungeons (MUDs), so it is definitely a use-case close to our heart :)
