There are many fun things to do in Vienna, if you are city focused. However, there are a lot of fun things to do just outside the city. The city of Vienna is surrounded by beautiful places that can be easily accessed via rail transport (regional trains). There are so many places one can go to hike and explore around Vienna, it would take a while to list them all. However, there is an interesting place anyone can spend a few days wondering around and find something new each day.
A small town of Bad Vöslau (map) is located about 35km south of Vienna, about 25 minute ride on the regional train. While the town is mostly know for being a spa town as well as hot spot of the red wine scene, the town is surrounded by beautiful forests and various hills. If you have a lot of time to spend and feel like relaxing than you should definitely check out the Vöslauer Thermalbad (map). This thermal bath house has been operating since 1873 and has many different pools.
Once you are ready to leave the luxuries of the thermal baths, you can head into the forest by following many hiking trail signs sprinkled throughout the town. Eventually you will end up at the Jubiläumswarte or the Harzberg tower. Constructed in 1898 for the occasion of the 50th jubilee of Emperor Franz Josef I. The tower provides stunning views of the surrounding area and as well as the mountain ranges around it. The tower offers a 360 degree view of breathtaking nature as well as full view of vineyards of Bad Vöslau. 
Once you are finished gazing over the horizon, you will find an interesting restaurant next to the tower, serving typical Austrian food. There are seating areas inside and outside. I highly recommend grabbing some coffee and enjoying the outside patio. On the cold day there are plenty of blankets around. The food is good, the service can be timely depending on how many people are inside. 
Behind the restaurant you will find something unique to the area. There is an actual kangaroo enclosure. While you wait for your food to come out, you can peek behind the building and find half a dozen kangaroos hanging out and relaxing. 
While these animals are probably wallabies, the smaller cousin of the kangaroo, it goes to say that the famous saying of „no kangaroos in Austria“ might not be completely correct. 