My family and I have been planing fir the same but in April, I can't tell if we would be able to go there at first place because of the post COVID-19 atmosphere.
I will share a few offbeat spots near Leh Ladakh see if it is suitable for your travel. Uleytokpo is a camping spot
Panamik is a small mountain village
Rumtse is on Leh Manali highway
Upshi is a camping spot near to Gompas