Austria other than Vienna

How small ? Innsbruck is in the mountains, with a funicular up to some grand views. Rick prefers nearby Hall.

Perhaps Salzburg?

Kitzbuhl, Seefeld they are in Tyrol so maybe too far away? Klagenfurt, Hallstatt also come to mind.

Please be aware that Vienna is not in the mountains nor is it near to the mountains. How far are you willing to travel? Is this a day trip or overnight?

Do you mean
-a small city that has mountains near it
-a small city with mountains, that is near Vienna?

If the first, then a couple options would be Salzburg or Innsbruck. Both have mountains easily accessible and viewable from town, and plenty of other things to do. Both are pretty touristed, but very nice. Innsbruck’s mountains are bigger / more the image of the Alps. These are both small cities, not little mountain towns.

" a small city with mountains nearby. " - Bolzano , in The South Tyrol , surrounded by The Dolomites , or Garmisch - Partenkirchen , in Bavaria , at the foot of The Zugspitze Bolzano - https://youtu.be/N06r3gge7-M Garmisch - https://youtu.be/GG2QYmV2lDU

Innsbruck is my most favorite city in Austria. If you run out of things nearby that interest you it is only a short train ride away from many other great towns in the mountains. Rent a car and you can explore all of South Tirol.

Take a Look at St Wolfgang on the Lake or St Gilgen,Hallstadt,Zell am See,Kufstein,Many choices out there.
Mike