I love the "State Park Camping Experience" in so many states. Generally, the sites are large; here in Michigan, they are nicely wooded, too.
Something I've discovered: I have been able to make reservations at "impossible" State Parks like Ludington, by simply checking the reservation system periodically. Many folks will make reservations a year out (and at first glance the park is "sold out") - but then are forced to cancel as "life" gets in the way of their camping.
I also agree that there ARE private parks with huge spaces - you'll just have to check their websites. The ones who offer large sites will be bragging about it :-)