Sebastian Kurz

Starting from the most official source there is on the internet: Wikipedia
and some gossip sites...

Sebastian Kurz
born 27 August 1986
single, together with Susanne Thier since their school time
grown up in Vienna, Meidling and at a farm of his familiy in Zogelsdorf
finished Realgymnasium Erlgasse in 2004

Residence

Farm

After a quick Google Image search for "Sebastian Kurz Zogelsdorf" I found two interesting images:

from the second image you can clearly see the house number and since Zogelsdorf is pretty small place the unique address is:
Zogelsdorf 7, 3730 Zogelsdorf

I controlled it with Google Maps and the position of the sun (shadow in the first pic).

Main

His main residence in Vienna was found in a similar style. After short browsing i found a video in which you could see the street name near his main residence.

Rotenmühlgasse

in a other scene you can even see the bell with his name on it.

Since Basti is not in the telephone book i tried the names of his neighbors.
A lookup at https://www.dasschnelle.at resulted in one person named Nechansky, Helmut who lives in the Rotenmühlgasse:

We can conclude that Basti lives at the Rotenmühlgasse 14, 1120 Wien (or near) in flat 15.

Acquaintance

Susanne Thier

His girlfriend Susanne Thier is on Instagram, her profile is private though.
She also prefers not to show up too much in public.

Parents

I did not find the name of the parents.

Marlene Dachsberger

Cousine.

Florian Tschandl

Tennis friend.