Have y'all ever been anywhere in Michigan? There are a lot of fun destinations "up north"! Mackinac Island, Traverse City, the Soo Locks, Whitefish Point, Sleeping Bear, etc. Most of our smaller trips are to northern Michigan, and in years when Easter falls later that can be a really nice time to head up there. Not so much when Easter is in March, though!
Chicago is a really fun town too. Get the
CityPass and look for a great hotel deal on Hotwire or Priceline and it can be surprisingly budget-friendly. The Field Museum and Shedd Aquarium were both hits with my kids, and DD loved the American Girl store.
A little tougher to do now that the passport rules have changed, but Toronto and the Niagara area are a lot of fun with kids. Toronto offers a CityPass too, and my kids just love Casa Loma and the science center.
One place we go back to time and again for short trips is actually in Ohio - Kalahari Resort in Sandusky. It isn't someplace I'd want to spend a full week, but for one or two weekends a year it is a really fun waterpark. Lots of slides and splash space for the kids, and a swim-up bar in the hot tub for the adults.

We go down to Toledo pretty frequently too; the zoo there is so much better than the Detroit zoo that it is worth the extra hour's drive, and we have a membership there so it works out to be a rather affordable overnight getaway.
Going a little further, more than 12 hours for us but maybe not for you depending on where in OH you're from, DC is very pretty in the spring and at least a little warmer than home. Lodging can be expensive, but the huge number of free attractions offsets that pretty nicely.
The rest of our trips down the east coast are to more summery destinations - VA Beach, Ocean City, the Outer Banks, Myrtle Beach, etc. - and I don't know how much would be open outside of tourist season. The drive down is half the fun on those kinds of trips. We've taken side trips to battlefields and caverns and all sorts of odd little stops along the way, in the tradition of the quintessential American road trip.