Are there any restrictions for accommodation in New York?

I've never heard of limits on how long you can stay in NYC. Perhaps he's confusing this with restrictions on how long people can rent a dwelling mostly aimed at peer-to-peer rentals like Airbnb

The New York State Multiple Dwelling Law, which covers buildings with three or more units, prohibits transient rentals of fewer than 30 days at a time, unless the owner is present for the time a guest is renting.

These laws are aimed at residents trying to rent their house/apartment. They don't affect you directly.

TL/DR: 10 Days in New York City is absolutely no problem in any way.

However, what you friend my be referring to is a collection of residency and rental rules that usually hit around the 30 day mark.

This is the distinction between a short term and long term rental which brings different rules and taxes.

Also, New York has some wonky tax and residency rules. I recall (fuzzy) a company I worked with would not allow non-New York residents to stay in New York for more than two weeks at a time and would not allow them to commute to New York for more than six months.

No there are no such restrictions, at least not for the city itself. Obviously you need a visa or other permission to enter the US, and there are restrictions on how long you can stay in the US, but not how long you can stay in the city.

Hostels may have a certain limitation on how long you can stay. For example, Hostelling International NYC has a maximum of 20 nights per calendar year (see http://hinewyork.org/about/faq/)