NYC has a Limited Use Vehicle reciprocity law. You are legal to ride an moped in NYC as long as you meet the registration, titling, and insurance laws of your LICENSING STATE.
Fact. So, if you've got a VT license, follow the VT rules for reg/ins.
If you have an NYS license, your vehicle, no matter where it's registered should meet the req's for the vehicle in the state, to avoid serious issue. AKA, plates/reg and insurance
As far as insurance, they don't care where the vehicle is registered when you pay them for insurance, only where it will used.
I have my XL175 regged in CT and my Cagiva in NYC, through the same company. I just had to physically get on the phone with them to explain and they were happy to setup sister accounts under the same customer (me).