Depends on exactly where you want to go and what you like to see. The Mammoth Cave in Kentucky as well as the Natural Bridge in southern Virginia are great stops. If you’re in DC, head to HIllwoodmuseum.org (for directions) which is a completely hidden gem in DC.

Bar Harbor maine is a beautiful lobster and vacation town.
Montreal is a great French city not far from the New England.
Toronto has the best Chinatown we’ve been to (better than San Fransisco). We feel it is the most cosmopolitan city here in North America and has a wonderful European feel with a warmth of Canadian hospitality.

Other things in DC are to definitely to the Arlington National Cemetery. If you get a day pass in the afternoon for the tourmobile and the tour, you can use the tour mobile all that afternoon and the following day but take the Arlington tour in the morning. The tourmobile is great because you can hop on and off between the Smithsonian museums and memorials.
The Spy Museum and the National Portrait gallery are close to each other and a short walk from the White House and definitely have lunch in the atrium of the portrait gallery since it is charming and a nice peaceful break in the city. While it is a long walk, you can start at the Lincoln Memorial, go to the Vietnam Memorial, then the Korean War memorial, the tribute to Martin Luther King, the WWII memorial which is incredible, and the Jefferson memorial.

Most people do not know to go around the side of the Lincoln memorial because there is a small history museum and gift shop as well as water fountains and bathrooms. The museum under the Jefferson memorial is another hidden treasure.

Lastly I highly recommend Mount Vernon and the Holocaust memorial museum.

Philadelphia has the Liberty Bell and has incredible constitutional history.
New York of course you should go to Ellis Island and also see the Statue of Liberty especially since it has had so much work done lately.

Hope that is a decent start.