Information about Graz:
Weather in September:
Usually sunny and dry, temperatures during the day around 20°C but chilly during the night (7°C). Nevertheless it is a good idea to have a rain jacket and a pullover with you.
In Graz nearly everything is in in acceptable walking distance. But there are also street cars and busses.
Picture from Wikipedia
Travelling by Airplane:
Graz has an airport which can be reachehed from several European cities: Airport Graz
The nearest Airport with many international connections is the Vienna Airport
From Vienna Airport to Graz:
To find your best travelling route please got the Austian Railway (ÖBB)
Fill it out as shown below with your personal arrival date and time (usually it takes less than 1 hour from landing to leaving the airport).
Calculate connection and fare and you can also book your ticket online. It might be a good idea at this time of the year to reserve a seat (possible during the booking process).