Don't go to the Gila Lower Box looking for formal campsites and places to hook up an rv. This is primitive camping at one of New Mexico's truest oases. 

Why? Because in 1990, cattle were prohibited from grazing this stretch of the Gila River. 

The result? One of the lushest, most verdant riparian environments left in the desert southwest.
For those with a 4wd or very high clearance, you can camp down along the cliffs right at the edge of the river corridor. Being a birders paradise, it's a very unique experience to sit on the edge of the cliffs, 20-30 feet above the tops of the cottonwoods and watch all the bird activity below. 

You can also watch bands of coatimundis grazing through the bosque. Watch out for rattlesnakes and Gila monsters during the warmer months though. 

I rate this as one of New Mexico's best outdoor experiences. (A note: I camp to the west of the location shown on the map.)