Rolled up without a reservation the day after Labor Day this year (9/4). Each camp spot had ample parking, and sectioned off portions of level gravel areas - one for table/fire ring and one for tents. So nice! We nabbed a spot overlooking the river, which you can hike along for about a mile. We were also able to see the Milky Way while sitting around the fire. Super nice spot.
HJ is a great campground for rafters. 20 mjnutes drive from Buena Vista. Fills up quickly, reserve early!