I second DC is great! Every summer, we head to the Lake Erie islands to South Bass (Put-in-Bay). It has a bad reputation for weekend partying, but during the week it is very family oriented and we just had a lodge for a week and found the campground was totally quiet on the weekend as well. What we do is camp, BUT to make it relaxing, we eat dinners and some lunches out or at the grocery, pick up the burgers to grill. Breakfast is coffee and simply things like muffins, granola bars, cereal. I buy the smallest milk when we land and pick up another daily. The island is small and the grocery is just up the road from the campground. There is also a chocolate/coffee shop within walking/biking distance, as is a golf cart rental. You can't beat $24/night on a bluff overlooking Lake Erie with the fresh air. The lodge we tried last year in comparison had hard-as-a-rock mattresses, if you want to call them that and were $700 for a week. The campsites we usually stay at are non-electric sites, which are nicer than the very small interior electric sites, but I take a very long extension cord, inflate the air mattresses and we carry them in to the tent. The campground is never as crowded, or full, like neighboring Kelley's Island, which is known as the family island. The campground also has kayak and jet ski rentals available, and this past summer, we picked up a $20 inflatable boat for him to paddle around in. He loved it! And since we'd forgotten his life vest, they provided him with one all week at no cost. The beach is a stone beach since that side of the island is very choppy, so be sure to wear the water shoes, flip flops don't cut it, and bring some beach chairs! Excursions to the neighboring islands are available too, as is parasailing which is so much fun. Each year we pick something like this during our 3-4 day trip (we typically go Sun-Weds).
Our next favorite is camping and canoeing at Mohican in Loudonville, OH. There are several campgrounds and we really like River Run. We get the rafts so we can all fit and be comfortable and pull two tubes connected with ropes behind us while canoeing. For about $75-100, canoeing is hands down a treat my kids love! There are lots of little "landings" along the way to get a hot dog, ice cream, and beverage with a potty break (purchase req'd, but that's half the fun anyway).