Crossword Genius

Crazy outing in Rome or New York, say, in touching relationship (10)

Ross

I believe the answer is:

contiguity

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'relationship' is the definition.
(thesaurus)

'crazy outing in rome' is the wordplay.
'crazy' indicates an anagram.
'in' is an insertion indicator.
'rome' becomes 'city' (I can't explain this - if you can you should give a lot more credence to this answer).
'outing' with letters rearranged gives 'ontigu'.
'ontigu' going into 'city' is 'CONTIGUITY'.

'or new york say in touching' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Guardian.
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