Just wanted to report back that I had some success in finding a suitable place to store my car for the off-season.
I was at first searching self-storage places but was not crazy about the idea about an outdoor unit that did not have any climate control for a vintage vehicle; yes it is out of the elements but who knows how well they keep pests or vermin from infesting the storage units.
I then Googled car storage in my area and came across a few solutions, one of which I decided to use. The location is aptlyl named Deluxe Car Storage and they are based in New Hyde Park, NY, about a 20 min ride from my place. The facility is brand new and very clean/well kept. The main storage area is climate controlled and all the cars are kept on battery tenders! They have a beautiful detail bay where the cars are washed and I am told a professional detailer comes in to clean the cars based on the package you choose. The staff is very friendly and professional and we worked out a lease where I can keep the car throughout the winter and they even offered a referral to an Alfa specialist in NY to look over the car and help me maintain it.
I must say I am quite happy with the experience and look forward to transporting my car there later this week after the holiday. I cannot ask for a better place to keep my car and more importantly, watched over until I can take it out again in fairer weather!
Hopefully my post helps another fellow member needing a similar solution!