Nocupholder
Try this place- Autosport Designs 631-425-1555,
www.autosportdesigns.com in Huntington Long Island, I know they store cars and are about 35 miles outside the city, but a ride on the Long Island Railroad to Huntington and then a short cab to them.
I used to bring my Morgan to them for service and would go downstairs to see all the exotics being stored for individuals., they have an incredible place with a lot of exotics for sale and they have a heated security “basement” where they store cars. I don’t know what they charge or what access you have to get your car when you want to stretch her out.
I also think that they would know of other places to store cars.
Another option would be to rent a garage in Queens at a private house, Queens is a short subway ride and you would have access 24/7 to your Cobra.
The North Shore of Long Island offers a lot of twisty roads and fun.
I also know of another place on the North Shore of Long Island were a buddy has stored his cars - will get back to you with that one when I reach him.
The city garages are no place for a Cobra, or the streets for that matter.
Rich