Ancient Karakorum is just one of the landmarks located 1.1 mi (1.7 km) from central Kharkhorin, so you might want to stop by for a few pics during your trip.
If visiting museums in Kharkhorin is on your list, you might want to visit the upcoming exhibitions at Kharakhorum Museum. If you want to experience more of the culture Kharkhorin has to offer, head to Ancient Karakorum, Erdene Zuu Monastery, and Great Imperial Map Monument.