I second a visit during Naadam. I did not see all of it, but what I did see was amazing

Few other neat places nearby-ish to ULN
Mongols Els - sand dunes. Family stay here - wonderful
Kharkhorin/Orkhon valley. Camped - wonderful
Göktürk museum - Orkhon area. Obelisk with first recorded word for Turk (or something like that)
Hustai National Park. Przewalski's horses/Takhi
Genghis (Chinggis) Khan relatives (?) - some sort of imperial ruins. There are random and one can walk through/over/around. Some have active archaeology digs while others are simply just there (for lack of a better way to describe the sites)

I have a bunch more info if folks are interested -