Vacation in Washington, D.C.:
Most of the hottest destinations in our nation's captial are 100% free! All of the monuments and memorials on the National Mall are free to visit, as are several of the museums and buildings around the mall including:
• The White House
• National Archives
• Holocaust Museum
• National Gallery of Art
• National Cathedral
• Library of Congress
• The Smithsonian Institute (includes 16 museums)
For the museums and attractions that aren't free, consider purchasing the Washington D.C. Power Pass, which gets you into the Crime Museum and Newseum (among others), as well as free bike rentals and bus tours.
Vacation in NYC:
As far as touristy cities go, New York actually has lots of free things to do. Visiting any of the city's parks (including Central Park, Washington Square Park and The Highline) is totally free, as is the Staten Island Ferry, which gives gorgeous views of downtown Manhattan and the Statue of Liberty. And while many museums charge for admission, most are donation-based (so pay what you want, you don't have to pay the recommended amount).
You'll be hard-pressd to see your favorite Broadway show for free (though some shows do run free promotions for students, check the show's websites for details), but the TKTS booth located in Times Square, downtown Brooklyn and South Street Seaport offers reduced tickets to same-day shows (matinee shows are sold the day before).
Here are some other free things your family can do in NYC:
• FIT Museum
• Grand Central Walking Tour
• New York Public Library
• The Bronx Zoo (pay what you want on Wednesdays)
• Socrates Sculpture Park
• Museum of Modern Art (aka MoMA, free admission on Fridays from 4 - 8p.m.)
• American Museum of Natural History (free admission the last hour of every day 4:45 - 5:45p.m.)
• Museum of the Moving Image (free admission on Fridays from 4 - 8p.m.)
Photo Credit: Flickr/ cdharrison