The Mongolian name "Tavan Bogd" means "five saints" and signifies the peaks of Khüiten, Nairamdla, Olgii, Bürged and Malchin. I really enjoyed exploring this remote, out-of-the-way place. It's like being in a completely different world, such is the sense you get of stepping back in time to the very dawn of man. The area's inhabitants – members of the Kazakh minority, and mostly Muslims – keep up the age-old traditions of Mongolian hospitality.
There are various itineraries you can choose to take from Olgii. Before heading further south, however, I recommend a detour to the site of Tsagaan Salaa in the northwest, where, across an area of some 15 km², there are more than 10,000 rock paintings created between the neolithic and the bronze age to be seen.
Next head to the national park in the south, where you'll be able to hike in the highest mountains in the whole of Mongolia. The ascension (non-technical) of Malchin Peak (4,005 m) is interesting: you can see the whole mountain chain from its summit, including the Chinese and Russian sections.