A property manager at least can handle things professionally with experience built over years.

I'm guessing that's a big yes... now of course too as long as you can handle the payment, have some repair reserves etc. even if you're not cashflow positive. 

Another point is, after over 40 years of handling tenant complaints, vacancies, large repairs, (last year my repairs totalled $111,618)  Maybe it's just time to scale down and lessen the headaches (I have 5 vacancies right now). 

In my understanding, the barrier to entry in the NYC market is so high and the market itself is mostly an appreciation play, making young people like me who just started out without much experience and capital almost unable to participate.

With one or two uncomplicated rentals, though, you really shouldn't be paying a CPA more than $1000 to handle your local, state, and federal tax returns.You find your lawyer the same way, by poaching an experienced investor's real estate lawyer.

Also, I agreed to handle any repairs under $1500.

Hello, I'm interested in understanding the responsibilities of a property owner that would not be handled by a property manager (or that would be a la carte items).

What's the best way to handle this?

I'm continually educating myself on the best point of entry.

If the tenant has an active renters insurance policy, most likely, their policy would handle the displacement.