I FIXED IT!!
For people who have this problem in future:
When trying to edit a file in Coda 2 it gave me a warning it couldn't edit a file in ~/Library/Caches/Coda 2 as it didn't have the right permissions.
I took a look and sure enough it was set to 'Read Only'. So I edited the permissions of ~/Library/Caches to to 'Read & Write' and BOOM, InDesign now launches.
Thanks to Panic for helping me diagnose Adobe's problems due to Apple's lousy Time Machine restore!
Note: Adobe, write clearer crash reports!