"Sorry, something went wrong" when trying to "Set up nearby device"
I had the same issue today. I had to replace my old (broken) Nexus 5X to a new Nexus 5X.

After unsucessfull tries (same error message as you) I started to all reconfigure manually when I noticed my old Nexus 5X was running Android 7.0 and the new stock Nexus 5X was still on Android 6.0. 

So here is what I did: I accepted the update to Android 7.0, then did a factory reset on the new phone and I restarted the procedure and it worked like a charm.