There is a nice spot for overnight stays near Davit Gareji Monastery, featuring a small lake. Accessing the lake may be tricky with a large camper, but a 4x4 vehicle can manage it. The border police may ask about your presence, but they are friendly. GPS coordinates may not be accurate.
A lovely location, but in 1930, four Border Police informed us we could not stay in the border zone and must return to Udabno. Communication was difficult as no one spoke English, leaving us uncertain about the reason. It could be a temporary issue.