Are most of New York's tourist attractions (museums, galleries etc.) open during the New Year holiday period?

Answer 1

yes but Christmas and New Years are leagal holidays and most likely closed those two days. Other days no problem. Lots of busy crowds to expect.

Answer 2

Yes. With the exception of Christmas day and New Year's day, you will find pretty much everything is open on a normal schedule.

In the U.S., the week between Christmas and New Years is not really a business holiday period like it is elsewhere. A lot of people take scheduled vacation time during that week, but most businesses don't close down.