The Salzkammergut is one of the most beautiful holiday regions in Austria, with its name coming from its history. As the premier spot for Salt ("Salz") Mining. As salt was and is important it was under direct control by the Emperors in Vienna - that's where the name "Kammer" came from.
The regional train has a comprehensive service running through the heart of the Salzkammergut and on into Styria. This provides easy access to the region from both Salzburg and Vienna, passing through Gmunden, Bad Ischl, Bad Goisern, Hallstatt and Obertraun.
I would however suggest car hire as the best way in which to explore this fascinating region. This gives you the freedom to explore area such as Gosausee and St Wolfgangsee, not accessible by train.
Schloss Ort - The TV series "Schlosshotel Orth" is playing there.
Skiing on the extensive Dachstein West Ski Region - 140km of Intermediate Piste + the Krippenstein Freeride Arena, for those looking for an exilhorating off-piste experience 
Swimming in the lakes
Walking on the Gmunder Promenade
Visit Hallstatt a UNESCO World Heritage site, a stunningly beautiful village.
The Dachstein Ice Caves at Obertraun, are well worth a visit.
Mountain Bike, there are many trails for all levels of biker with stunning scenery around every corner.
The Krippenstein is a stunning paragliding site, rising 1500m from the valley floor.
Steckerlfisch - fish on a stick grilled on open fire