I've camped at Harriman State Park, but it was a planned overnighter leaving from NYC, so I had reservations. It was last summer (2009) during the heatwave - it looked to me like there were some open sites, but it was pretty full. The rangers were friendly enough and I couldn't imagine them sending you off on your own on a bicycle at night just because the campsites are "full." At the very least, you could probably find somebody agreeable to the idea of letting you set up a tent on their site for just one night.