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.