Hiking activities in Central Mongolia
This approach to Tsetseegün from the south side is the easiest route by far. As you face the monastery, cut over to your right (east) until you get to the stream. Just follow the stream until it nearly disappears and then head north. About three hours' walking should bring you out over a ridge into a broad boggy meadow, which you'll have to cross. If you've walked straight to the north, the twin rocky outcrops of the summit should be right in front of you.
When you start to see Ulaanbaatar in the distance, you're on the highest ridge and close to the two large ovoo (a shamanistic pyramid-shaped collection of stones as an offering to the gods) on the summit (GPS: N47°…
This is the easiest route on the Ulaanbaatar side, mainly because you hit the fewest boulders. However, this route is also the least interesting. The walk to Tsetseegün and over to Mandshir takes about six hours. The problem is that getting to the Observatory ('Khureltogoot' in Mongolian) is difficult. You could catch a bus to Nalaikh and get out at the toll gate, then walk the last 6km up the hill. Otherwise, you'll have to take a taxi.