I’m going to overlay this with some of my ideas of the post Reaper War situation, but this is a great map that saves me a lot of work. It’s by Daniel (Neon Knight) at the Cartographer’s Guild forum and I was turned onto it by Brainclouds.
For a rough guide, without access to the relays a ship could travel a maximum of around 5000 light years, presuming comparability to modern sea vessels (1/20th of galaxy diameter) and that would be a top of the line ship. Travelling that far would take not much short of a year. Another limiting factor is needing planetary systems to discharge the built up charge of the core into at regular intervals. Even if a non-stop trip could be made with a ship like the Normandy SR2 it would take 20+ years to cross the galaxy after the loss of the relays.
Postmortem Studios 
I have just cottoned on to you doing this conversion.
If you are thinking post-reaper. How are you going to interlink the populated systems?
Also most of the inter-stellar communications were relay-based. That would mean that the only viable comms would be those based on quantum entanglement which are hugely restricting (each pair is unique and cant talk to anyone else). You could get round this by having a quantum ‘exchange’ and the exchange performing a bridge between pairs, but everyone would have to be commited to using the same exchange. It is kinda like old telephone exchanges.