The Sept 11th Museum is now open in downtown NYC however they charge $24/adult.
The good news is they offer a small number of free admissions on Tuesday evenings from 5 p.m. to 8 p.m. The last entry is at 7 p.m. A limited number of tickets are available for online reservation two weeks in advance of each Tuesday evening starting at 9 a.m. Same day tickets are available at the ticket windows starting at 4 p.m.
The bad news is they get grabbed up really quick. I was able to get 4 tickets this morning for 6/3 but I saw the available times disappearing in front of my eyes. (I then realized that's Shavuos and will have to give away the tickets, oh well.)
Here's the link for the Free Tuesday tickets:
http://visit.911memorial.org/WebStore/shop/ViewItems.aspx?CG=fat1&C=fat2