On a budget stuff to do- Go to Times Sq, Grand Central (get kids their own subway maps to bring home- free!- my niece framed hers when she left lol), Rockefeller Plaza-. All free. Chinatown has a million and one really cheap NYC souvenirs (5 tees $10 etc.). Take the SI ferry & see the Statue of Liberty. It's free! The 9/11 Memorial is also free ( or for a donation of your choice). Get passes ahead of time & print them out at home.
http://visit.911memorial.org/WebStor...=WSCG&C=TKTCAT
I'll think of more...