The Bulgan aimag Museum  on the main street has some information on obscure sights in the aimag; a display on J Gurragchaa (Mongolia’s first man in space), war photos and a few musical instruments, including the ol' human-femur-cum-wind-instrument (known as a kangling or ganlin). The ethnography section features a red-eyed wolf and a demented-looking lynx; elsewhere there are a few period surgical instruments that'll make you glad you live in the 21st century, plus some airag (fermented mare's milk) churners and saddles.
The Museum of Ancient Things (Ugsaatny Zizuyn Salvar) has a few ethnographical exhibits.