For beginners I can only recommend the climbing route in Gosau, directly at the Lake Gosau (see image).
More climbing routes for advanced climbers are directly in Hallstatt and the surrounding ares (the Seewand-route is only recommended for strong and skilled persons. The Sissi-climbing-route should also be tried only by experienced climbers.
Equipment can be rented at „Janu – Sport 2000″ in Hallstatt.
There are two companies that let you book organised climbing tours:
Laserer alpin OG in Gosau
Outdoor Leadership (Heli Putz) in Bad Goisern, also for Tandem-Paragliding from the Krippenstein.