@Aymeric De Conde Where in NYC are you looking in?
If you are not planning to live in NYC for a long time then I think you better off investing in an area with a better cash flow...If you have in mind your next destination after NYC then you should probably research that area...NYC is like investing in bonds...very safe...but very low if any returns...Managing an apartment in the city can be quite difficult. I have 2 rental coops which I purchased after the crash...and recently purchased a house in PA...for turning over a 380sf 1BR in NYC I got a quote for $1700 (grout and paint)...while in PA I got $4800 for a 2000 sf 5BR house...In NYC with that money you are a little fish and it is even hard to find contractors to come give you a quote...in general knowing what I know now I would go to PA, Upstate or the Midwest if I could do it again.
Another factor...as mentioned by other is that with this money you are mostly limited to coops...It is quite hard to find those which allow subletting and for many of those it is even harder to get financing.
Management is another issue that have to be considered as all co-ops (and many condos) will demand to approve your tenants causing unnecessary delays whenever there is a turnover.
On the flip side...appreciation is great and vacancy is as low as it gets.
In your position I'll focus on one or two other markets and compare them to the deals you find in NYC.
I do agree with you in NYC (Manhattan especially) you'll never have problems finding tenants and while rental returns may be low appreciation skyrockets. The best situation as a landlord in NYC is when you find out the value of your home 10-15 years after purchasing it and realize that if you were to do it again you cant afford to buy them.
As for repair costs. In NYC, the best person to do repairs in a co-op building is the live-in super especially for things like tile, grout repair, fixtures installations and paint. They will do it correctly, no board approval for vetting the contractor and the super won't charge you nearly as much as a contractor. Plus, the super is likely not to charge you for small future (backed up drain, change plumbing or electric fixtures) repairs because you established a relationship with him. Just be good to him around Christmas time.
Contractors in NYC are expensive because it goes with the territory and labor rates are highest in the nation. A NYC electrician will charge $100/hr and in PA its $20/HR.