The Piedra River between Pagosa Springs and Durango has a number of places to boondock on the river. There is a small Forest Service campground just off of the highway on the west side that doesn't have any hookups but has some very nice campsites plus a vault toilet and hand pump for water. The campground is relatively cheap per night. If you follow the road on the east side for several miles there are several spots to boondock where the road crosses the river about 5 or 6 miles in.
The fly fishing isn't super, but there are definitely fish in the river.