Töv aimag has a network of good unpaved and paved roads, so you can easily use public transport to make day or overnight trips from the capital.
For the other aimags, share jeeps will travel from the nearest provincial centre to other destinations, but off the main paved road traffic throughout these regions is light. In Övörkhangai, public transport will get you to Erdene Zuu Khiid, Khujirt and Arvaikheer, but if you want to visit Tövkhön Khiid or Orkhon Khürkhree you’ll need your own transport. Horse is the best way to reach Naiman Nuur. In Arkhangai, the main road is one of the few routes in Mongolia where hitchhikers can easily get to a few places of interest, including Taikhar Chuluu and Terkhiin Tsagaan Nuur.
A jeep is fine for getting around, but travelling by horse grants the best access via the river valleys and into the mountains.