I wouldn't visit all 3, and if you do I wouldn't do it in that order (go Boston-NYC-DC or the reverse). You'll have a more enjoyable visit if you cut out one and allow yourself some more time in the other two.
DC and NYC are especially easy to get around using public transportation. Boston is not bad.
DC - visit the Smithsonian museums, Arlington cemetery, view the White House, tour the capitol, and visit some of the monuments (Lincoln, Jefferson, Washington, Vietnam, Korea, WWII, etc).
NYC - see a show, Central Park, Times Square, an observation tower (Top of the Rock is my favorite), 9/11 Memorial and Museum, Statue of Liberty and Ellis Island.
Boston - Freedom Trail, Boston Common, Old North Church, Paul Revere House, Harvard's campus, harbor cruise.
All 3 have baseball parks if you want to catch a game. Yankee Stadium (NYC) and Fenway Park (Boston) are iconic baseball locations.