All state parks are dry- I've never been hassled while camping because we aren't morons about it (and have rarely gone camping without, lol), but i HAVE seen groups kicked out for being obnoxious, diesel-fuel-on-the-bonfire, hooting-n-hollering at midnight drunks. Just take plastic cups, you'll be fine.
the cabins at Atsion are literally 2 minutes from the main trails everyone uses when they go back in Wharton. There's also primitive camping, as well as camping with water and flushies right along the same road, with lake access to swimming (bring a canoe!)
My personal favorite is Bodine Field, you can camp on the Wading river, put an inner tube in at your campsite, and after about an hour-n-a-half climb out and walk 10 minutes back to your site. There's lots of rope swings on the way down river, too. it's primative, though- outhouses and a water pump. Maybe not so good for a first time camper. It IS only a 15 minuted drive to Batsto village, though, which is fun if you are a history buff!
Other than that, just about any spot in Wharton you find a primative campground, you are right on easy wheeling trails. at the end of July in the Pines, though, the greenheads get real bad. We were actually gonna hit Bodine the weekend of the 19th, after that it's not so friendly.
there's also www.wadingpines.com
, down actually next to Bodine (and another primative campground). you'll pay way more for the same exact area, but it might help to take a first-timer someplace with water and electric on hand, and real bathrooms you can walk too.