We can start with a nice walk from Ober St. Veit (a part of 13th district which used to be a village and still keeps its appealing authenticity, so it is good to take a look at the nice old houses and the church) up to the entrance to Lainzer Tiergarten (St. Veiter Gate), go through it to Hermesvilla (a beautiful building from the beginning of the 20th century — a present from Emperor Franz-Josef to his wife Sissi), take a good look at it's surroundings (a beautiful park) and maybe insides (the entrance costs 8 € but it's quite worth it because you can see the opulent and stylish interior of the villa together with many valuable antique furniture/pieces which used to be there originally).
Afterwards, we can enjoy the walk to the exit from Lainzer Tiergarten (Lainzer Gate): The way goes through the large park grounds and past a natural reservoir where you can see lovely does. Then, after 10-15 minutes of walking through this nice part of 13th district, we will reach Mauer (also formerly an independent village) from the upper side and take a walk behind the wine gardens from the hills and enjoy the view of the city over the grape plants — a really beautiful combination!