Kharkhorin's museum is small, but highly impressive – probably the country's best museum outside Ulaanbaatar. Everything is beautifully designed and well displayed.
The exhibits include dozens of artefacts dating from the 13th and 14th centuries that were recovered from the immediate area, plus others that were found from archaeological sites in other parts of the aimag, including prehistoric stone tools. You'll see pottery, bronzes, coins, religious statues and stone inscriptions. There's also a half-excavated kiln sunk into the museum floor.
Perhaps most interesting is the scale model of ancient Karakorum, which aims to represent the city as it may have looked in the 1250s, and is based on descriptions written by the missionary William of Rubruck. Don't miss the doco detailing the excavation of the 6th century tomb of Shoroon Bumbagar, which is located 220km from Kharkhorin.
The building is fully air-conditioned, there are free English-speaking guides available, English captions throughout and free wi-fi in the small cafe (although the cafe itself is disappointing).