Which route are you taking, as there could be several ways to come?
We would be taking I81 most of the way
You might find some historical and scenic places to visit in the Virginia I-81 corridor or nearby, like Shenandoah Valley.
I don't know much else, but maybe someone else will who can reply.
The smokey Mtn's are a good suggestion- they are probably too young to appreciate D.C. but there are excellent exhibits at the smithsonian for kids. Detour off on the Blue ridge parkway in Virginia for a few hiking opportunities. Depending on when you are coming, the Virginia creeper trail in Abingdon is great for biking and there are often festivals around abingdon. Drive by the iconic Bristol motor speedway- they used to let you walk out on the track but probably not any more.
It is possible to drive several different routes, depending on time and your children. There is Charlottesville, Virginia. Home of UVA and a beautiful southern town. Lauray Caverns in Virginia, Dollywood and Gatlinburg. Almost here, there is The Lost Sea.
The Blowing Rock area is filled with excellent children's activities. Tweetsie Railroad, gem mining, parks, music, walking, hiking and Grandfather Mountain.
Thanks for your suggestions, I'm going to map it all out
Not too very far from I-81 in central Virginia (Google has it at 1-hour 25-minute drive from I-81) is the very small town of Appomattox Courthouse, VA. There is not much to do there but see the exact same buildings where General Robert E. Lee surrendered his Army of Northern Virgina to General U.S. Grant of the U.S. Army thus beginning the end of the US Civil War.
Go see Shenandoah National Park!!
It is GORGEOUS, and much much less crowded than the Smoky Mountains, plus basically on your way. Very convenient to I 81.
If your kids love outdoors, plenty to do and a perfect break. Not sure where in NY you are starting but it probably a little under half way. If you are looking for just a one night stay, you may not be able to get lodging in the park, unless its Monday, Tuesday, or Wednesday. But you can easily find hotels on the interstate at Harrisonburg, Staunton. Charlottesville may be higher rates.
There are some easy hikes, and that time of year ought to have beautiful flows in the waterfalls and blooming flowers ( big meadow ought to be amazing then) Baby wildlife, etc. Plus most National parks have Junior Ranger activities etc. for littles.
One visit we were on the Limberlost trail and at the beginning saw a group of trail riders. The guides horse was spooked by a rattlesnake, so the guide shot the rattlesnake. Then midway down the trail, we spotted a mama bear and two cubs about 40 yards away. We were nowhere near our car! Talk about adrenaline...
Anyway we were driving home from a trip in DC where we had seen all the amazing things there, and to this day, that one day of our Shenandoah stop is all my kids talk about from that vacation.
Haven't seen bears again there, but the beautiful scenery is still there as always.
Have a wonderful trip.