Tumut is a town in the Snowy Mountains region of New South Wales.
Australia doesn't have much in the way of mountain peaks. The Snowy Mountains mostly consist of the high country, where elevations slowly rise up to around 1600m at the alpine villages, with much of the area being a largely a plateau. Even Australia's highest point, doesn't really give the experience of a mountain. The flat topped piece of ground rises only a few metres higher than the second highest "mountain" only a few kilometres away, and while the country is pretty, the vista is less than that you would get from the sandstone cliffs in the Blue Mountains.
The best place to get the mountain peak experience in the Snowies is on the Snowy Mountains highway between Tumut and Cooma. The roads wind through the mountains, and you can get some appreciation for the height of the peaks, and the drop on the side of the range.
Most of the attractions are out of town, and you will need a car to see them.