Am I correct that NYC is positioning itself as coin with no transaction fees?
Correct!
Then what is the motivation for miners to process the transactions once all new New York Coins will be emitted? How will the network sustain itself?
I'm a large NYC bag holder and I want to clarify this question
NYC, unlike BTC, has unlimited emission. If we agree to reduce block reward, we can make a constant 1%/year "inflation", less than USD and others fiat currency