One of my favorite spots in Vienna is Kahlenberg/Leopoldsberg. Berg means mountain or hill. From Donau Park you can see both Kahlenberg and Leopoldsberg.
How to reach with public transport?
You can easily reach both the places with public transport. Both these places come under zone 100 of public transport. Zone 100 is for Vienna. Bus 38A from Heiligenstadt will take you to both the places. Heiligenstadt is the last station in U4 metro train. The bus will reach first Kahlenberg and then it will go to Leopoldsberg. Sometimes the bus will stop at Kahlenberg itself and will not go to Leopoldsberg. So watch out for the bus board while onboarding. You can walk from Kahlenberg to Leopoldsberg as well in less than 30 minutes.
Alternatively you can also hike from Kahlenbergerdorf to Leopoldsberg and then from Leopoldsberg to Kahlenberg through the vineyards. I once went in my bicycle in this route and loved it.
What is there?
At Kahlenberg :
First of all you get a pretty view of Vienna. You can easily see the main canal of Danube river, and also Donauinsel and AlteDonau, Riesenrad (giant wheel) at Praterstern.
There are few shops to buy souvenirs, a cafe, a restaurant. Do carry cash with you. There is no bankomat (ATM) at either Kahlenberg or Leopoldsberg. And from what I have seen the shops or the cafe do not accept cards.
At Leopoldsberg :
There is a church. You can take a leisurely walk around the church. You will get views of Vienna which you would not get from Kahlenberg.
From both Kahlenberg and Leopoldsberg there are walking trails present. Try them out.