To see firsthand where some of your tax dollars are wasted- take a bus or subway to 46th St and 1st Ave to see the UN..
I wouldn’t miss Ellis Island either:
http://www.ellisisland.org/genealogy/ellis_island_visiting.asp
Since you’ll be there for St Patrick’s Day- the parade is worth seeing- it starts at 11 AM on 44th St and 5th Ave..and speaking of- regardless of your religious beliefs- a MUST see is St Patrick’s Cathedral @ 51st St and Madison Ave..
Thanks for the street adresses too.