I know you said cheap, but Plimoth Plantation is pretty freaking cool and very educational. It's about to close for winter, but will open again in March. You can even pay extra and get to spend the night in one of the houses in the village or even
sleep on the Mayflower.
Edit: I just saw it's $600 per night per house, so never mind. But a day visit is very cool.
We went when the kids were about that age, and they loved it.
If you just want to go camping, and spend time out doors, I think you'll find that a lot of campgrounds are closed for the season. For example, the Maryland state parks closed their campgrounds last weekend. I think the National Park campgrounds stay open.