To reach East Green Mountain from Christmas Valley, take Millican Road north from Christmas Valley HWY. Cut over to Crack in the Ground Rd or alternatively take Crack in the Ground Road from Christmas Valley HWY. Crack in the Ground road is not paved, but fine for passenger vehicles.
I recommend stopping at Crack in the Ground Road for some Geo-Tourism. It is a short ~1mi out and back hike. Crack in the Ground is as the name describes and is a very cool fissure in the basalt.