The options for overnight trips are endless as we live in such a great area that allows us to travel to a variety of places from DC in a short amount of time (although sometimes those car rides seem forever).

Lancaster, Pennsylvania (about 2.5 hours from DC)

Winchester, Virginia (1.5-2 hour drive from DC)
Rocking S Ranch
Dinosaur Land
Shenandoah Valley Discovery Museum
Wilsons Wild Animal Park

Theme Parks
Hershey Park
Six Flags
Kings Dominion

Natural Bridge, Virginia (under 4 hours from DC)
Natural Bridge State Park VA has been designated as a Virginia Historical Landmark and a National Historical Landmark. Natural Bridge VA is located in the Shenandoah Valley.
Dinosaur Kingdom II
Virginia Safari Park
Caverns at Natural Bridge
Great Valley Farm Brewery

Eastern Pennsylvania (2.5 hours from DC)
Longwood Gardens: American botanical garden. It consists of over 1,077 acres of gardens, woodlands, and meadows in Kennett Square, PA.
American Helicopter Museum
Oasis Family Fun Center

Philadelphia (under 3 hour drive, Amtrak accessible)

Calvert County (under an hour drive from DC)
Anne Marie Sculpture Garden
Calvert Marine Museum
Pirate Adventures on the Chesapeake
Calvert Cliffs State Park
Solomon’s Island
Chesapeake Bay Outdoors
Chesapeake Beach Railway Museum
North Beach

Reader recommended campgrounds and hiking:
Little Bennett: Montgomery County’s only campground
Fun activities include laser tag, pedal cart track, movie nights, crafts, big jumping pillow and so much more for families. Enjoy miles of hiking, biking and trails throughout 3,700 acres of forests and meadows. With more than 25 miles of trails to explore, 91 wooded campsites from which to choose, 3 cabins, 3 yurts and a variety of weekend activities available in season for all age groups and interests, Little Bennett Campground is a perfect weekend getaway or vacation spot.
Cherry Hill: Closest campground to Washington, DC.
You can rent a cabin, pod, yurt, pitch a tent or pull up your RV. On-site amenities include 2 pools and a splash park to tractor rides, movie nights, and 18-hole mini-golf.
Camp Twin Creeks
Bushkill Falls
Cabins in Virginia

Beach & State Park day trip