How do I go about registering a moped in nyc?

You can ride a Class C moped in NYC if: (1) Your moped is: registered and insured. (2) Equipped with a headlight that stays on while riding. .(3) You carry any class of driver’s license.. (4) You wear eye-protection and a helmet at all times. (5) The moped can travel no faster than 20 mph..

I would probably do it through the New York DMV, but maybe I'm just not very adventurous with that stuff.

Look it up on the N.Y. DMV website. To answer your question, that is what most people here would have to do.

To register a moped in NY, you must first call the Technical Services Bureau at 518-474-5282 and see if your moped is on their DMV certified list and what class it is. If it isn't on their list, you can't register it in NY. Next you need a tracing or photo of your VIN, or verification from a police officer.

Once you have done that, go here.  https://dmv.ny.gov/registration/register-moped

The vehicle must be on the list of DMV approved Class C limited use motorcycles.

I cannot find the list on the Internet.

I'm not sure either. The DMV however, they would know