Tennis
In Gastein valley, there are 36 tennis courts. And in Bad Gastein alone there are 21 (and one squash-court).
There is thus ample opportunity to train your backhand, easily. The local tennisclub have courts only 800 metres from Schillerhof. Right next to Spar market.
Each summer, there is a major WTA tournament with many international stars. On that occasion, a "Centre Court" is built at Stubnerkogel.