Very far from town - but very beautiful and peaceful!
There are a lot of dipsersed camping spots all along Hermosa Park Rd north of Durango. Some are even an hour drive (4WD) from town. These spots are far from one another so you feel like you have the mountain to yourself! Good water flow as well if you need it. I wouldn't recommend it if you plan to visit waterfalls and other attractions in Durango since it is such a drive. Definitely stay more than a couple nights!
Month of VisitJune