Gobi (or gov' if you are translating from the modern, Cyrillic spelling) actually means "semi-desert". Most of it isn't the sand dunes that people expect to see. It's more like scrub-land, on which it is possible to graze animals.
Omnogov' aimag (South Gobi province) is where most tourists get taken. It has some interesting sites, such as The Flaming Cliffs, where Roy Chapman Andrews, a famous paleontologist first found dinosaur eggs in the 1920s. These are some photos from from trip there with a Smithsonian tour group, when I was their Study Leader.