Getting there & away
To get to Khögnö Khan Uul from Kharkhorin by jeep, turn north off the main road, 80km east of Kharkhorin. The road passes several ger camps until, after 8km, you reach Khögnö Khan ger camp, where you turn right for the remaining 4km or so to the monastery ruins. There is a shortcut if you are coming from Ulaanbaatar (turn right after the Bichigt Khad ger camp).
There is no public transport to the monastery but you can take a Kharkhorin-, Khujirt- or Arvaikheer-bound minivan from Ulaanbaatar, get off at the turn-off on the main road (T5000) and then hitch (or more likely walk) the remaining 12km.