For the best camping experience in the area, I would recommend the 20 Mile overnight canoe trip in the Delaware Water Gap National Recreation Area. This trip is a leisurely paddle, with amazing views, small sets of class 2 rapids, and pristine riverfront camping. You can choose many different sections of river for the trip. Lots of people like to end at Kittitanny point. I begin at Dingmans Access, and end at Smithfield Beach as I find this to be the most scenic section of river. Along the way, there are dozens of primitive camp sites to choose from. The sites are only accessible by boat, and there are no roads, bridges or houses along the way, just you and the Bald Eagles, which often build massive nests near campsites.
I recommend NOT going on a Saturday night, as the campsites are available on a first come, first serve basis and tend to fill up rather quickly. If you must go on a weekend, you will want to book one of the Alosa campsites that can be reserved. If you have a group, you will want to book one of the group sites available along the way. There are several. Valley View Campsite, Rivers Bend Campsite, or Worthing State Park, which is also a car campground. These offer bathrooms and picnic tables, but have nothing to buy, so you will want to bring plenty of water, and firewood.
There is a helpful PDF published by the National Park with the camping regulations and a map. You will want to call a local outfitter for current river conditions and suggestions on how to manage the logistics of the one way paddle.