Just my opinion, but this isn't a good domain.
"New York City" is tops. 3.1 million references in Google.
NYC is second BEST. 2.5 million references in Google.
"NY City" is "okay". 67,100 references in Google.
"Ny City Ny" pulls up 868 references.
The amount of people that "respond" to this abbreviation will be low. I think most people will this it just looks odd.
It's odd enough to make a good domain branding, but this becomes the case where the advertising effort (and content) will do more to empower the site than the domain ever will.
$150
~ Nexus