In reply to cliff: There is a klettersteig in Innsbruck. Take the cable car out of town up on to the ridge, there is a big alpine route on the ridge. Easy access, cable car to the start. Google Insbrucker klettersteig.
There is a great one to the west of Innsbruck, by the airport, it is grade D/E and goes up a huge bit of rock. It's called Kaiser Max
http://www.bergsteigen.at/de/touren.aspx?ID=62
topo
http://www.bergsteigen.at/pic/pdf/62_Topo_296_kaisermaxtopo.pdf
The alpspitze is good, there is an easy one to the summit, plus a grade D/E on a nearby hill, all serviced by a cable car (Alpspitzebahn)
One problem might be your timing though, some of the cable cars shutdown for a period at the end of summer.
St Anton has a great alpine route, C/D, cable car start, google alberger klettersteig
Bargsteigen is the best source of routes, the topos are great,
http://www.bergsteigen.at/de/kst.aspx?ID=2
when searching use the German word klettersteig rather than the italian Via Feratta